Q1-1-05-Barrera rampa.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Cálculo de coeficientes de transmisión y reflexión por una barrera tipo \"Rampa\""
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "\n",
    "\n",
    "Fuera de la barrera, \n",
    "\n",
    "$$\n",
    "-\\frac{\\hbar^2}{2m}\\frac{\\partial ^2 \\psi(x)}{\\partial x^2}  -E \\psi(x)=0\n",
    "$$\n",
    "\n",
    "de manera que las soluciones serán de la forma $A e^{{\\bf i}k x}+ B e^{-{\\bf i}k x}$, correspondiendo a una energía $E=\\frac{\\hbar^2 k^2}{2m}$. Si estamos interesados en un flujo de partículas que vienen desde $x\\ll 0$, esperamos que la forma asintótica de la solución en la región $x\\gg a$ sea\n",
    "$$\n",
    "\\psi(x)=A_{r} e^{{\\bf i}k (x-a)}\n",
    "$$\n",
    "\n",
    "En la zona de la barrera, \n",
    "\n",
    "$$\n",
    "-\\frac{\\hbar^2}{2m}\\frac{\\partial ^2 \\psi(x)}{\\partial x^2} + (V_0 \\frac{x}{a}-E) \\psi(x)=0\n",
    "$$\n",
    "con la condición de que $\\psi(a)=A_{r}$ y $\\psi^{'}(a)={\\bf i} k A_{r}$.\n",
    "\n",
    "![Esquema de la barrera de potencial.](figs/qI-1-05-grafico-barrera.png)"
   ]
  },
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   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Para resolver la ecuación diferencia, conviene hacer el cambio de variables  $x \\rightarrow z= (x-x_0)/\\alpha$, con\n",
    "\n",
    "$$x_0=\\frac{a k^2}{k_0^2}$$\n",
    "$$\\alpha=\\sqrt[3]{a/k_0^2}$$\n",
    "$$k_0= \\sqrt{\\frac{2 m V_0}{\\hbar^2}}$$\n",
    "\n",
    "de manera que  $\\psi(x)=\\varphi((x-x_0)/\\alpha)=\\varphi(z)$. \n",
    "\n",
    "Aquí, $x_0$ corresponde al **punto de retorno clásico** de la partícula en el potencial para la energía dada, suponiendo que $a\\rightarrow \\infty$. Si $0<x_0<a$ diremos que el punto de retorno es *real*, mientras que si está fuera de la barrera tendremos un punto de retorno clásico *virtual*. Por otro lado, $\\alpha$ una escala de longitud efectiva, que depende del potencial. Observamos que $(a/\\alpha)^3=\\frac{2 m a^2 V_0}{\\hbar^2}=a^2 k_0^2$, de manera que esta cantidad será pequeña si $V_0$ es pequeño frente a la energía cinética mínima de un estado concentrado en la barrera.\n",
    "\n",
    "Con este cambio, la ecuación diferencial se reduce a \n",
    "$$\n",
    "\\frac{\\partial ^2 \\varphi(z)}{\\partial z^2} - z \\varphi(z)=0\n",
    "$$\n",
    "que se conoce como **Ecuación de Airy**. Las soluciones son combinaciones lineales de las **Funciones de Airy**  $Ai(z)$ y $Bi(z)$. Estas funciones pueden escribirse también como\n",
    "$$\n",
    "Ai(z)=M(z)\\cos(\\theta(z))\n",
    "$$\n",
    "\n",
    "$$\n",
    "Bi(z)=M(z)\\sin(\\theta(z))\n",
    "$$\n",
    "\n",
    "con $M(z)$ y $\\theta(z)$ dos funciones monótonas.\n",
    "\n",
    "\n",
    "![](figs/qI-1-05-airys.png)\n",
    "\n",
    "## Propiedades de las Airy\n",
    "\n",
    "\n",
    "Con la normalización usual, estas funciones tienen los siguientes límites:\n",
    "\n",
    "|     Función     |    $z\\rightarrow 0$    |  $z\\rightarrow \\infty$ | $z\\rightarrow -\\infty$ \n",
    "| :---------:     |   :-----------------:  | :---:  | :---: \n",
    "|    $M(z)$       |    $\\frac{2}{3^{2/3} \\Gamma \\left(\\frac{2}{3}\\right)}(1+\\frac{(\\frac{3}{2})^{1/3}\\sqrt{\\pi}}{\\Gamma(1/6)}z)$    |  $\\frac{1}{\\sqrt{\\pi}z^{1/4}}e^{\\frac{2}{3}z^{3/2}}$  |  $\\frac{1}{\\sqrt{\\pi}(-z)^{1/4}}$ \n",
    "|    $\\theta(z)$  |         $\\frac{\\pi}{6}-\\frac{ 3^{5/6}\\Gamma(2/3)}{2 \\Gamma(1/3)}z$   |$\\frac{1}{2}e^{-4/3 z^{3/2}}$ |   $\\frac{\\pi}{4}+\\frac{2}{3}\\sqrt{-z^3}$  \n",
    " \n",
    " "
   ]
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   },
   "source": [
    "![](figs/qI-1-05-masympt.png)\n",
    "![](figs/qI-1-05-theta-asymp.png)\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Derivando la identidad $\\tan(\\theta(z))=\\frac{Ai(z)}{Bi(z)}$ respecto de $z$, encontramos además que\n",
    "$$\n",
    "\\theta^{'}(z)=\\frac{-W(z) \\cos^2{\\theta}}{Bi(z)^2}=\\frac{-W(z)}{M(z)^2}\\,,\n",
    "$$\n",
    "donde $W(z)=Ai(z)Bi^{'}(z)-Ai^{'}(z)Bi(z)=\\det(^{Ai(z)}_{Ai^{'}(z)}\\;^{Bi(z)}_{Bi^{'}(z)})$ es el *Wronskiano* asociado a las soluciones. De la antisimetría,  la bilinealidad del determinante, y de la ecuación diferencial que define a $Ai$ y $Bi$, $\\frac{dW}{dz}=0$ y por lo tanto $W(z)=W(0)=\\frac{1}{\\pi}$. De esta manera,\n",
    "$$\n",
    "\\theta^{'}(z)=\\frac{-1}{\\pi M^2(z)}\n",
    "$$\n",
    "\n",
    "y \n",
    "\n",
    "\n",
    "$$\n",
    "Ai^{'}(z)= M(z)\\left(\\frac{M^{'}(z)}{M(z)}\\sin(\\theta(z)) - \\frac{\\cos(\\theta(z))}{\\pi M^2(z)}\\right)\n",
    "$$\n",
    "\n",
    "$$\n",
    "Bi^{'}(z)= M(z)\\left(\\frac{M^{'}(z)}{M(z)}\\cos(\\theta(z)) + \\frac{\\sin(\\theta(z))}{\\pi M^2(z)}\\right)\n",
    "$$\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Cálculo de los coeficientes de transmisión"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Conviene entonces escribir la solución de la ecuación de onda con energía $E=\\frac{\\hbar^2 k^2}{2 m}$ como\n",
    "\n",
    "$$\n",
    "\\psi(x)=\\left\\{\n",
    "\\begin{array}{l r}\n",
    "A_l e^{{\\bf i}k x}+B_l e^{-{\\bf i}k x}   &  x <a \\\\\n",
    "\\left.u Ai(z)+v Bi(z)\\right|_{z=\\frac{x}{\\alpha}-(k \\alpha)^2}             &  0 \\leq  x\\leq a\\\\\n",
    "A_r e^{{\\bf i}k (x-a)} +  B_r e^{-{\\bf i}k (x-a)}   & x>a\n",
    "\\end{array}\n",
    "\\right.\n",
    "$$\n",
    "\n",
    "\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Escribimos las condiciones de continuidad en $x=0$\n",
    "\n",
    "$$\n",
    "\\left(^{Ai(z_l)}_{Ai(z_l)/\\alpha}\\;^{Bi(z_l)}_{Bi(z_l)/\\alpha} \\right)\\left(^{u}_{v} \\right)=\n",
    "\\left(^{1}_{{\\bf i k}}\\;^{1}_{-{\\bf i k}} \\right)  \\left(^{A_l}_{B_l} \\right)\n",
    "$$\n",
    "\n",
    "y en $x=a$,\n",
    "\n",
    "$$\n",
    "\\left(^{Ai(z_r)}_{Ai(z_r)/\\alpha}\\;^{Bi(z_r)}_{Bi(z_r)/\\alpha} \\right)\\left(^{u}_{v} \\right)=\n",
    "\\left(^{1}_{{\\bf i k}}\\;^{1}_{-{\\bf i k}} \\right)  \\left(^{A_r}_{B_r} \\right)\n",
    "$$\n",
    "\n",
    "donde $z_l=\\frac{a}{\\alpha}$ y $z_r=\\frac{a}{\\alpha}-(\\alpha k)^2$. De esta manera,\n",
    "\n",
    "\n",
    "\\begin{eqnarray*}\n",
    "\\left(^{A_l}_{B_l} \\right) &=&\\left(^{1}_{{\\bf i} k}\\;^{1}_{-{\\bf i }k} \\right)^{-1}\\left(^{Ai(z_l)}_{Ai^{'}(z_l)/\\alpha}\\;^{Bi(z_l)}_{Bi^{'}(z_l)/\\alpha} \\right)\n",
    "\\left(^{Ai(z_r)}_{Ai^{'}(z_r)/\\alpha}\\;^{Bi(z_r)}_{Bi^{'}(z_r)/\\alpha} \\right)^{-1}\n",
    "\\left(^{1}_{{\\bf i }k}\\;^{1}_{-{\\bf i }k} \\right)  \\left(^{A_r}_{B_r} \\right)\\\\\n",
    "   &=&\\frac{\\alpha^2}{2{\\bf i}k \\alpha W(z_r)}\\left(^{{\\bf i} k}_{{\\bf i }k}\\;^{1}_{-1} \\right)\\left(^{Ai(z_l)}_{Ai^{'}(z_l)/\\alpha}\\;^{Bi(z_l)}_{Bi^{'}(z_l)/\\alpha} \\right)\n",
    "\\left(^{Bi^{'}(z_r)/\\alpha}_{-Ai^{'}(z_r)/\\alpha}   \\;   ^{-Bi(z_r)}_{Ai(z_r)} \\right)\n",
    "\\left(^{1}_{{\\bf i }k}\\;^{1}_{-{\\bf i }k} \\right)  \\left(^{A_r}_{B_r} \\right)\\\\\n",
    "   &=&\\frac{\\pi}{2{\\bf i}k \\alpha}\n",
    "   \\left(^{{\\bf i} k \\alpha}_{{\\bf i }k \\alpha}\\;^{1}_{-1} \\right)\n",
    "   \\left(^{Ai(z_l)}_{Ai^{'}(z_l)}\\;^{Bi(z_l)}_{Bi^{'}(z_l)} \\right)\n",
    "\\left(^{Bi^{'}(z_r)}_{-Ai^{'}(z_r)}   \\;   ^{-Bi(z_r)}_{Ai(z_r)} \\right)\n",
    "\\left(^{1}_{{\\bf i }k \\alpha}\\;^{1}_{-{\\bf i }k \\alpha} \\right)  \\left(^{A_r}_{B_r} \\right)\n",
    "\\end{eqnarray*}\n",
    "\n",
    "con $W(z)=\\det\\left(^{Ai(z)}_{Ai^{'}(z)}\\;^{Bi(z)}_{Bi^{'}(z)} \\right)=W(0)=\\frac{1}{\\pi}$\n",
    "es el Wronskiano asociado a las funciones de Airy, y donde usamos que\n",
    "$$\n",
    "\\left(^{a}_{c}\\;^{b}_d\\right)^{-1}=\\frac{1}{\\det \\left(^{a}_{c}\\;^{b}_d\\right)}\\left(^{d}_{-c}\\;^{-b}_a\\right)\n",
    "$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Consideremos ahora el coeficiente de transmisión $T$ para una partícula que se mueve desde la izquierda. En tal caso, $B_r=0$, y $T=\\frac{|A_r|^2}{|A_l|^2}$.\n",
    "\n",
    "Consideremos varios límites."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Bajas energías"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Si $k \\alpha\\ll 1$, \n",
    "\\begin{eqnarray*}\n",
    "\\left(^{A_l}_{B_l} \\right) &\\approx&\n",
    "\\frac{\\pi}{2{\\bf i}k \\alpha}\n",
    "   \\left(^{0}_{0}\\;^{1}_{-1} \\right)\n",
    "   \\left(^{Ai(0)}_{Ai^{'}(0)}\\;^{Bi(0)}_{Bi^{'}(0)} \\right)\n",
    "\\left(^{Bi^{'}(a/\\alpha)}_{-Ai^{'}(a/\\alpha)}   \\;   ^{-Bi(a/\\alpha)}_{Ai(a/\\alpha)} \\right)\n",
    "\\left(^{1}_{0}\\;^{1}_{0} \\right)  \\left(^{1}_{0} \\right)\\\\\n",
    "&=&\n",
    "\\frac{\\pi Bi^{'}(a/\\alpha)}{2{\\bf i}k \\alpha}\n",
    "   \\left(^{Ai^{'}(0)}_{-Ai^{'}(0)}\\;^{Bi^{'}(0)} _{-Bi^{'}(0)} \\right)\n",
    "\\left(^{1}_{-Ai^{'}(a/\\alpha)/Bi^{'}(a/\\alpha)}  \\right)\n",
    " \\\\\n",
    "&=&\n",
    "(Ai^{'}(0)Bi^{'}(a/\\alpha)-Bi^{'}(0) Ai^{'}(a/\\alpha)) \\frac{\\pi }{2{\\bf i}k \\alpha}\n",
    "   \\left(^{1}_{-1}\\right)\n",
    "\\end{eqnarray*}\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Si $a/\\alpha \\ll 1$ (barrera delgada), $Ai^{'}(a/\\alpha)\\rightarrow \\frac{1}{3^{1/3}\\Gamma(1/3)}\\approx -0.26$, $Bi^{'}(a/\\alpha)\\rightarrow \\frac{3^{1/6}}{\\Gamma(1/3)}\\approx 0.45\\, ,$ y \n",
    "$$\n",
    "\\left(^{A_l}_{B_l} \\right) \\approx\n",
    "{\\bf i}\\frac{a^2}{4 k \\alpha^3}\\left(^{1}_{-1} \\right)={\\bf i}\\frac{a^2 k_0^2}{4 k a}\\left(^{1}_{-1} \\right)\n",
    "$$\n",
    "\n",
    "de donde obtenemos, para el coeficiente de transmisión, $T\\approx \\frac{16 k^2 /k_0^2 }{a^2 k_0^2}$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Por otro lado, si la barrera es ancha, $Ai^{'}(z_r) \\rightarrow 0$, $Bi^{'}(z_r)\\rightarrow \\frac{e^{-2/3 (a/\\alpha-(k \\alpha)^2)^{3/2} }}{\\sqrt{\\pi}\\sqrt[4]{a/\\alpha}}$ y\n",
    "\n",
    "\n",
    "\\begin{eqnarray*}\n",
    "\\left(^{A_l}_{B_l} \\right) &\\approx&\n",
    "{\\bf i} (0.23 \\frac{e^{2/3 (a/\\alpha-(k \\alpha)^2)^{3/2} }}{\\sqrt[4]{a/\\alpha}k \\alpha})\n",
    "   \\left(^{1}_{-1}\\right)\n",
    "\\end{eqnarray*}\n",
    "\n",
    "de manera que $T\\approx 18.9 (k \\alpha)^2 \\sqrt{a/\\alpha} e^{-4/3 (a/\\alpha-(k \\alpha)^2)^{3/2}}$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Límite de altas energías"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Para altas energías, $z_l < z_r \\ll 1$, por lo que podemos usar la aproximación asintótica para las funciones de Airy:\n",
    "\n",
    "\\begin{eqnarray*}\n",
    "Ai(z)&\\rightarrow &\\frac{1}{\\sqrt{\\pi}(-z)^{-1/4}}\\sin(\\frac{\\pi}{4}+\\frac{2}{3}\\sqrt{-z^3})\\\\\n",
    "Bi(z)&\\rightarrow &\\frac{1}{\\sqrt{\\pi}(-z)^{-1/4}}\\cos(\\frac{\\pi}{4}+\\frac{2}{3}\\sqrt{-z^3})\\\\\n",
    "Ai^{'}(z)&\\rightarrow &- (-z)^{1/2} Bi(z) \\\\\n",
    "Bi^{'}(z)&\\rightarrow & (-z)^{1/2} Ai(z)\n",
    "\\end{eqnarray*}"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "De esta manera, definiedo $\\theta_{^l_r}=\\frac{\\pi}{4}+\\frac{2}{3}\\sqrt{-z_{^l_r}}$,  podemos escribir la ecuación matricial como\n",
    "\n",
    "\\begin{eqnarray*}\n",
    "(^{A_l}_{B_l})&\\approx&\\frac{1}{2{\\bf i}k \\alpha (z_l z_r)^{1/4}}\n",
    "   \\left(^{{\\bf i} k \\alpha}_{{\\bf i }k\\alpha}\\;^{1}_{-1} \\right)\n",
    "   \\left(^{1}_{0}\\;^{0}_{\\sqrt{-z_l}} \\right)\n",
    "   \\left(^{\\sin(\\theta_l)}_{-\\cos(\\theta_l)}\\;^{\\cos(\\theta_l)}_{\\sin(\\theta_l)} \\right)\n",
    "\\left(^{\\sin(\\theta_r)}_{\\cos(\\theta_r)}   \\;   ^{-\\cos(\\theta_r)}_{\\sin(\\theta_r)} \\right)\n",
    "\\left(^{\\sqrt{-z_r}}_{0}\\;^{0}_{1} \\right)\n",
    "\\left(^{1}_{{\\bf i }k \\alpha}\\;^{1}_{-{\\bf i }k \\alpha} \\right)  \\left(^{A_r}_{B_r} \\right)\\\\\n",
    "&\\approx&\n",
    "\\frac{1}{2{\\bf i}k \\alpha (z_l z_r)^{1/4}}\n",
    "   \\left(^{-{\\bf i} k \\alpha}_{-{\\bf i }k\\alpha}\\;^{-\\sqrt{-z_l}}_{\\sqrt{-z_l}} \\right)\n",
    "   \\left(^{\\cos(\\theta_r-\\theta_l)}_{-\\sin(\\theta_r-\\theta_l)}\\;^{\\sin(\\theta_r-\\theta_l)}_{\\cos(\\theta_r-\\theta_l)} \\right)\n",
    "\\left(^{\\sqrt{-z_r}}_{{\\bf i }k \\alpha}\\;^{\\sqrt{-z_r}}_{-{\\bf i }k \\alpha} \\right)  \\left(^{A_r}_{B_r} \\right)\\\\\n",
    "&\\approx&\n",
    "\\frac{\\sqrt{k \\alpha}}{2{\\bf i}   \\sqrt[4]{1 - k_0^2/k^2}}\n",
    "   \\left(^{-{\\bf i} }_{-{\\bf i }}\\;^{-1}_{1} \\right)\n",
    "   \\left(^{\\cos(\\theta_r-\\theta_l)}_{-\\sin(\\theta_r-\\theta_l)}\\;^{\\sin(\\theta_r-\\theta_l)}_{\\cos(\\theta_r-\\theta_l)} \\right)\n",
    "\\left(^{\\sqrt{1 - k_0^2/k^2}}_{{\\bf i }}\\;^{\\sqrt{1 - k_0^2/k^2}}_{-{\\bf i }} \\right)  \\left(^{A_r}_{B_r} \\right)\\\\\n",
    "&\\approx&\n",
    "\\frac{-\\sqrt{k \\alpha}}{2   \\sqrt[4]{1 - k_0^2/k^2}}\n",
    "   \\left(^{e^{{\\bf i }(\\theta_r-\\theta_l)}(\\sqrt{1 - k_0^2/k^2}+1)}_{e^{{\\bf i }(\\theta_r-\\theta_l)}(\\sqrt{1 - k_0^2/k^2}-1)} \\;\\;^{e^{{\\bf i }(\\theta_r-\\theta_l)}(\\sqrt{1 - k_0^2/k^2}-1)}_{e^{{\\bf i }(\\theta_r-\\theta_l)}(\\sqrt{1 - k_0^2/k^2}+1)}\\right)\n",
    "  \\left(^{A_r}_{B_r} \\right)\n",
    "\\end{eqnarray*}\n",
    "\n",
    "Finalmente, \n",
    "$|A_l|^2 \\approx |A_r|^2\\frac{k \\alpha}{4 \\sqrt{1-k_0^2/k^2}}(\\sqrt{1 + k_0^2/k^2}-1)^2$, \n",
    "$|B_l|^2 \\approx |A_r|^2\\frac{k \\alpha}{4 \\sqrt{1-k_0^2/k^2}}(\\sqrt{1 - k_0^2/k^2}-1)^2$\n",
    "y por lo tanto,\n",
    "$$\n",
    "R= \\frac{|B_l|^2}{|A_l|^2}\\approx \\frac{(\\sqrt{1 - k_0^2/k^2}-1)^2}{(\\sqrt{1 - k_0^2/k^2}+1)^2}\n",
    "\\approx \\frac{k_0^4}{16 k^4}\n",
    "$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
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     "end_time": "2018-09-17T12:26:59.961217Z",
     "start_time": "2018-09-17T12:26:57.194930Z"
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   },
   "source": [
    "![](figs/qI-1-05-transmision-1.png)\n",
    "\n",
    "![](figs/qI-1-05-transmision-2.png)\n",
    "\n",
    "![](figs/qI-1-05-transmision-3.png)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Generación de gráficos"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2018-09-20T12:46:34.725347Z",
     "start_time": "2018-09-20T12:46:34.224207Z"
    }
   },
   "outputs": [
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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "%matplotlib inline\n",
    "import matplotlib.pyplot as plt\n",
    "plt.rc('text', usetex=True)\n",
    "import numpy as np\n",
    "\n",
    "\n",
    "x3s=np.linspace(-3.2,-1.4,100)\n",
    "wf=.1*np.exp(-(x3s+2.4)**2/.25)*np.cos(20.*(x3s+1.8))+1.\n",
    "plt.plot(x3s,wf,color=\"b\")\n",
    "\n",
    "x3s=np.linspace(-1.2,.7,100)\n",
    "ks = np.array([ 20.*(1-x) if 0<x<1 else 20. for x in x3s])\n",
    "wf=.095*np.exp(-(x3s+0.2)**2/.25)*np.cos(ks*(x3s))+1.\n",
    "plt.plot(x3s,wf,color=\"orange\")\n",
    "\n",
    "x3s=np.linspace(1.1,2.9,100)\n",
    "wf=.03*np.exp(-(x3s-1.8)**2/.25)*np.cos(20*(x3s+1.8))+1.\n",
    "plt.plot(x3s,wf,color=\"green\")\n",
    "\n",
    "\n",
    "\n",
    "xs=np.linspace(-3,3,100)\n",
    "vs=np.array([1.3*x if 0.<x<1. else 0 for x in xs])\n",
    "plt.xlabel(\"$x/a$\")\n",
    "plt.ylabel(\"$V(x)$\")\n",
    "plt.text(1.2,1.2,\"$V_0$\")\n",
    "plt.plot(xs,vs,color=\"red\")\n",
    "plt.arrow(-2.2,1.15,.5,0.,color=\"b\",shape=\"right\",head_width=.05,head_length=.15)\n",
    "plt.arrow(.1,1.15,-.5,0.,color=\"orange\",shape=\"left\",head_width=.05,head_length=.15)\n",
    "plt.arrow(1.7,1.15,.5,0.,color=\"green\",shape=\"right\",head_width=.05,head_length=.15)\n",
    "\n",
    "plt.savefig(\"figs/qI-1-05-grafico-barrera.png\")\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Graficos de las expresiones asintóticas"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2018-09-20T12:46:35.529404Z",
     "start_time": "2018-09-20T12:46:34.727434Z"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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tmVs+KCWgUCgUa6Tf089fPP8X3FR7E8f2H0s/OT8Ic/1XdDwAlBJQKBSKNeEL+/joyY9SYi3h8/d8Hpslw7ve/5R87bx3k2e2OlRMQKFQKFZJOBbm4099nNHFUf7xnf9IQ2lD9kX9J6GsAWp3b/4EV4GyBBQKhWIVxOIxPvXTT/H8+PN8+vZPZ8cBAOJx6H9aWgGattlTXBVKCSgUCkWeCCH4qxf+ip8M/oSPH/g4v7j9F40vnHgdAnNXfDwAlDtIoVAo8iIu4vzl83/JYxcf48P7Psxv7vtN84v1eMC2ezZjagWhlIBCoVCsQCQe4U+f/VP+vf/f+e19v83Huj+W+4b+k1C7B1yNmzPBAlBKQKFQKHKwEF7gT575E54dfZaPdX+M37nxd3LfEAnC0PNw4MObM8ECUUpAoVAoTBjyDfG7T/w+IwvDfPr2T3N45+GVbxp+AaLBKz41VEcpAYVCoTDgH176Nv/rzF8TjUF47Lf4+mIjNWKKe3fV5b7x8tOydXT7HZsz0QIpODtI07TDmqYd0jTtEybnH0q8Hs33HoVCodgqAtEAv/adP+GLZ/8UIjV8qOXzHLvtnUwvhvjNr7zEZ75/llhcmA/Q/3SidbRr8yZdAAVZApqmdQMIIU5omtapaVq3EKIn47KjmqYdBo6t4h6FQqHYdHome/iTp/4rk4ERGng3//of/pwKhwOAj75jB3/1g3P8488usxCM8NAH9qNl1gAEvTDWA3d/fAtmvzYKdQc9CDye+L4fOARkCvQjQogTq7xHoVAoNg1vyMsXTn+Bf730rxCtpDH8B3zvd34Le5E1eU2xzcKf/fwNuBxF/N0Tl2h2O/nYoR3pAw08K1tHXwWpoTqFKgE3MJfyc7XBNd0JbdkthPhsnvcoFArFhhOJR/jWpW/xxVe/iDfkpc36bi713smXfv++NAWQyh8d2sHInJ+/feIiBzsquXN7zfLJy0+DzQGtt23Sb1A4G14xLIT4bMISqNY07VA+92iadlTTtJc1TXt5enp6g2eoUCiuN4QQPDH0BL/0nV/iM89/hg5XB3/91v/N2TP38Dt37mJHfbnpvZqm8Zfv30dXbRn/+V9eZSEYWT7Z/zS0vRVsJab3X2kUqgQ8QFXiezcwm3oyEQDWc6pmgc6V7gEQQjwihDgohDhYW1tb4BQVCoVCEovH+NHAjzjyvSP84ck/RNM0/u7tf8dXf+6rfOcFjbJiG0ff1rniOM5iG58/chNTCyE+/+ML8uDCJEyfg86rxxUEhbuDHgUOJr7vBE4AaJrmFkJ4kD7//sT5LuBh4GWjexQKhWKjCEQD/PDyD/nKm19hwDdAh6uDz9z5GR7ofACbxcbwnJ8fn53gd+/twu0szmvMm1vd/Ppb2/m/zw/y/u4Wbp5/Rp64iuIBUKASEEL0aJp2MOHm8aRk+TwBHEicP6pp2hzQp583uUehUCjWlUHfIP9y4V/4du+38YV97Krcxefv+TyH2g5htSz7/L/2whAa8KtvaV/V+H/8rl386MwEn/7Om3y75Sk0ewU03rTOv8XGUnCxmBDiEYNjB1Y4n3VMoVAo1gN/xM/J4ZN8t++7nBo7hU2z8Y72d/DLu36ZA/UHstI6Q9EY//LyMIf21NPkdqzqWeX2Iv7kXbv548deJeB/EmfH3WAxDihfqaiKYYVCcdUTjUd5ceJFvt/3fU4MnSAQDdBY2sjv3vy7HN5xmFqneWzxmYszzC2F+dBtbWt69vtvaeYHT5/C6Rsj0vGHXLm7CRujlIBCobgq8Uf8PDf2HE8OP8nTI0/jDXkpLyrnPdvewwOdD9Bd341FWzn35XuvjVHpLOKuHTUrXmuE1aLxyd2T8CJ817uDD6xplK1DKQGFQnHVMOwb5tTYKX429jOeH3ueYCyIq9jFPS33cF/bfdzdcjcl1vzTM/3hKI+fneT93c0UWdeeLLlzqYc5SzX//aUY770vZlpjcCWilIBCobhi8Ya8vDzxMqfGTnFq7BQjiyMANJY28v4d7+cdbe+gu76bIsvanDBPX5gmEInxwP4C+v4LAYOniLXdyfT5MP/vxSE+fOe2tY+3ySgloFAorgiEEIwtjdEz2cOrU6/SM9VDr6cXAKfNyW2Nt/Fre3+NO5ruoN3Vnt23Zw2cvDCFy27jto6qlS82Y64fFieovfftvCVUxT883ceHbmu7aqwBpQQUCsWWsBhe5NzcOc7OnuXNmTfpmephyj8FQFlRGTfV3cS7t72bA/UH2F+7f82rfTOEEDx1YZq7d9ZiK8AVxOAp+dp+Jx+rrOZXvvwCj740zG/c0bEu89xolBJQKBQbzmJ4kfNz5zk78ARnB09yJu5nMOxBIFsy1zvrOVB3gFvqb6G7rpvt7u1pefwbwdlxH1MLIe7dWWBXgsFT4KyGmp3cXgO3baviS0/18uCtrVeFNaCUgEKhWDeC0SCXvZfp9fRyyXOJ3vleej29jC+NJ6+pi0bZGwrznqpd3HDnJ9lbs5cax9oycwrhqQuyL9k9uwpVAs/KDWQ0DQ34w3fs4Ff+9wv8y8vD/PrtHQXPc6NRSkChUKwKIQRzwTmGFoYY8A7w+mQfPx04i58RlmKTxIkDYLPY6Kzo5Ja6Wzji+iV2Pfcwe8NRan77GXjxYXjmc3CTF1o3XwEAPHVhin3NLurK7WsfxDsCnkF4639KHrq9q5pbOyr5h6f6+OVb2yi2bXifzoJQSkChUGShC/qxxTEGFwYZ8g0x4BtgyDfEoG+QxchiysUW4pEq4qF66uzdfPK+e9lVtZNWV+uyH/+Vr8FkP3zoUSirhXs+Cee+B0/+Jex6L1g2V1B6AxF6hjz8p3u6Chto8Dn5mrKVpKZp/N7bt/ObX3mJb78yygdvbS3sGRuMUgIKxXWIEILZ4Cxji2OMLY4xujgqv18aSx4LxoLJ6zU0msqaaHe180DnA3RUdNBW3sbXfubn5JsRvvcH93Bu3MfHvvEq0zfs5t2dHekPfPFhqLsBdr5L/my1wV3/Gb51VPbg73r75v3ywEuX54jFxZoLxJIMPgslLqjfl3b4np213NhcwZee6uWXupsLCzxvMEoJKBTXGLF4jLnALFOBaSb9k0z5p5jyTyW/n1iaYHxpnFAslHZfRUkFTaVNdFZ0clfzXTSVNdFU2kSbq42W8pasIqxxb4DHXz/Jb97Ryc76cnbUlfG154d4+Ol+fuW2tmXBN3UOxl+Dd38WUtM69/4C/OCP4Y1vbroSeHFgjmKrhZtb3YUNNPis3D8gI4itaRq/f992jv3Taf79jXF+4ebmwp6zgSgloFBcJUTjUeaD8/TNjbMU9eKPedKE/LRfCv0Z/ySxjHutmpUaRw11zjq2u7dzT8s9NJU10VzWLIV9WROlRaWrms/3XxsnFhf82ltl501N0/itu7bxkX8+zTOXprlvd7288Nz3AA1u+KX0AYrssPsBef6B/7GpG7G8eHmOm1orCsveWZyGmYtw868anr5/Tz0768v44sle3re/CYul8LqGjUApAYViCwlGg8wF55gNzDIbnE37fjaQ/rMn5DEco7yonDpnHbXOWt6ilVLv8VLnaqdu+hL1b/l96m49RpW9at1TLr/3+hg3NlfQUbOsPO7bXUd5iY0fvTmxrAQuPQ7N3TIWkMmNH4DXvi6v2fPAus7PDH84ypujXo7ds/LmMTkZWq4PMMJikbGBj33jVX5ydpKf29dQ2PM2CKUEFIp1QAjBYmQRT9CDxzeMJ+TBQwxvyCu/T/nSj3lDXgLRgOF4ZUVlVNmrqHZUs61iGwfqD1CEi6/+dJa2ijoW/CWIaDk//oMHqLCXyZtCC/CFG6Djbnjwn+GrD8BL/xfu/MS6tzcenF3i9REvn3r37rTjxTYL79hTx+NnJ4nG4thCHhh9Gd72CeOBtt0LJRVw6SebpgReGfIQjQtu21bg9uaDp6DImXP/gAf2N/G3Jy7x9ycv8a4b6telynm9UUpAoUgQF3H8ET8L4QV8YR8L4QX5FVlIOzY0P8uF6SnKnSFi2hKekAdfyEdURA3H1dBwlbhwl7hxl7ipd9azs3Jn8udqRzXV9uqk0K+yV2G3Zactfub7Z4l6Bvjq0bdzYXKBD3/lJU6c8fCBAwklcO57EPTCHR+Vvvc7Pwpf/yD0Pg6737uu79WT52Vl73tuzO6583P7Gvj2q2O8ODDHHf6nQMRhx/3GA1ltsO1u6H9qXeeXixcuz2HRoLutwHjA0HPQfABs5juRWS0a/+meLj7xr6/z1MVp3r6rrrBnbgBKCSiuCeIiTiAaYCmylP61MMaid5iF0ip8CWGe+aUL98XIInERz/kch81JIFhELOpA8zm5s7Od7vpuKdCLynH/9Au4Y3EqNBvuSBD3f3yacmdtwa6YWFzwnVdHeecNcuOTxgo7HdVOvvXKKB840CIvevPfwN0OrbfJn7veAaW1MvC6zkrghf45WiodtFY5s869bWctxVYLJ89PcUf0JDgqoekW88E674Xz34e5y1C18Y3XXro8xw1NFZTbC2hDEV6CiTfhrj9a8dJfvKWZ//nEJf7+yV7u3Vl7xVkDSgkotoxYPIY/6s8W3Ct9RZdYCi+/zgcXiMSDoIkVn+m0OSkvLqe8uBxXsYs6Zx1d7q60Y/r3yWNF8lhZcRmf+/ElvvxMP48eu53f+D8v4qys59PvSgi48/8OU0PwwX+CkjL4p/fD5Z/BjYcLfq9eGphjZjHMA/ubABmEfWB/E196qpf5pTCVJcDAz6D715czcKw22PEuOP89iEXlz+uAEIIXB+ZMV7XOYhs3t7p5cWAexIvQ+pbc7qjOe+Vr/1MbrgQisTivDM/zK7etbhvJLMZeARFbVrg5KLZZ+Mg9nfzpd87wfP8ct3cV6IZaZ5QSUOQkLuIEo0H8UT+BSEC+RgPJr+TPkUDW8enFBS5Nz1FTDhZrZPn68CKB8AKhPBdENs1GaXEppbZSnEVOyorKqCipoLGskUCwiCdHvYhYCZqw80fvuJFWdyWlRaWUnvoSzsHncFV2Uj55lrLfexlb5do//LG44F9Pj3D/3npu7ajiA90tPHZ6mKVQlNISm1yJO2tg13tAs4C7DV5/dF2UwDMXp7FZNN6W0ufmvj11/P3JXn7WO8P7KocgGpCulVR2vhNe/WcYPQ1tbyl4HgCXphaZWwrzlk7zzpu3bavi60+/BsUXYf+DuQes3g6uZlkvcPDD6zJHMy5MLBCMxLmlUFfQ8AvyteXWvC4/crCVv3uyl78/eUkpAcX6EIlHCEaDhGKhtNdgLEgoGpKvBseS18aCDM55mFpcpNFtJU4kIcz9+BfHCERDBKw2gvHwquZls9hw2Bw4rA6mfYJotJippRLe2tFAY1kjDqsdx8Wf4Fj04RCC0q5DlO56jxTaqV+2Uin4i0opthSbmtC/97UeHAszfOt37+TQ/3ia+YltfKR7DwTm4eJTcOA34I4/gL/dLwXyPSYByjx4dXiemcVw0g/+vpua+KfnBzl5YYoHbqhL+N4fWF5x73oPnP4qRAJQtLq9azM51TfLTa1uykqWP7L7mytw2W387NIM76v7qTyYmanSlqhkHX5h3ZTAC/2zALw1R2D1tm1VvPn0JflD6wrP1TSZaz/0/LrMLxevjcgMq4LrA4Zfguod4MyvBbW9yMrRuzv5bz84R8/QPN1tlYU9fx1RSqAAhBCE42FCsRDhWJhAJERUhAnH5FcoFiK8NEUYCFmtaccj8YixAI+FCEVDBGIBQtEQEwsLeIJ+XA6ICv36ILEVfNdm2Cw27FY7NksJcwsCIWzMBp3srKvCVeKiIRbD4ZnGIQQOVzOOm34bp80pBXuRQ75mfDltzuQ5vU3AN14c4pP/9gb/5T17+G8/OMeB3bv5yD1dMNoDT3wR3vs3cPa70PcyvPd/r6ltQDAS48S5SX751la21ZRyz85afvjmBJ989260vichFoIbPyhX5C23Sr9zAUrg6QvTWDS4N+EG6W5zU15i49neWR6oGpdB2e2Hlm/Yfj+88A8yi2T7O9b83GAkxhujXj6SkdJos1o42FFFz9A8+H8mq1YzhVJZLVR1Lq9c14GeIQ915SW0Vpkrtu72Sl63XiKOFUtz98qDttwGb/4reEehYuNrKfQAAAAgAElEQVQKq14b9lBVWkxLZQFKWQgYeRF2vntVt/3KW9r40lO9fPHJXv7xN/OzIDaDgpWApmmHAQ/QLYT4rMH5o4lvu4QQxxPHHhJCHNc07agQ4pFC52DEq1OvshhZTAropFCOhZlZWmJo3kdLVRExIYVxOOglPH2esKuRkK0o/Z54+v2pgrxQLJqFEmsJdqsdu80uv0+8ingRIzNFiHgNxdEyfm5vKyW2Euz9T2Mfe50SIbDveCcle34eu82O3bp8v91ql9cmjjlsDkqsJckA5Z999wxff2OIIwdb+NoLQ3zjgXtpry6Fr7wHYhVyBX3iz+Ddb4e6Pav+vX745gTbakr5nbu38d3XxvjRmxNSCZz7HlhssO8wFJXCtz8C46/ILItV8sLlOULROPfulkL57bvrePL8FH3TS2zvexLsbpmfDrJdwZOfgaUZKF1bq4CXBubZ2+SiwiEVnc1q4S2d1Zzqm4GGM/KilB4ytCY+6KM9BSmBs+M+YnHB/pbs1evNrW5+emEM4X8BrfvXjQdofau0UoRIr9hdI2+MetnfUpEzwFlWYuMuez+DbGNbcR5FaLpbZeSlDVYCXm5aYe4rMtcP/tnlv2+elJbY+K07t/E3j1/kzJiXG5oq1j6HdaQgJaBpWjeAEOKEpmmdmqZ1CyF6Us4fAk4IIfo1TXtM07RDQogTwNGE8jhW0OxzcPyZ44wtjeWe/7gVh62EYmsxxUEfJdEQxQuDFNfuosRqp9hajLPISYm1hGJLMcXWYvm9Nf17n1/wv04OIYQc77MfOEBpUQnF3/0oJb4xigUU3/mHlNzya+n3WoqxWWym/5Cf+f5ZXhof5D/evY0vnuzjQ+97G9vdVvjR5+HmD4FnGC4+Bw/846o+3EIIvv/6GPfvrecj93TxtReG+PGZCY7eWiXT3u7+uFxBn/gzuPijVSuBQDjGc/2z/Ie3yN2f3rm3nr95/CKziyGq+0/KD7zDvSwYLz+zJiVwqm+GIquWdEu8LdEH5oXLs2wf+Bl03LUckOy4S74OPQd73rfqZ+kBxQ/d1pZ2/NaOSk6cmyR8+RTFlR1QnlIQZK+Amp0yT74A3hjxArC/JVto3NTqZhvjaNEAtBw0HqD1NlmQNdcP1YU1TPOHo/RNL/Jeg9TQNIRgZ/wyP4jdSntcrFwt23AjWEukErjhFwuaoxmLoSgXpxZ4940FFm0NvyhfV3JzGfDrd3TwyDP9fPFkL1/61dX/z28EhVoCDwKPJ77vBw4BPSnnOxNfjyTO6/bskYQy2DA+d8/nEAiKLemC+9QlD3/4jTPYbcXE4xZOfuo+qn3n4JF7pEk69CK87QurWrl99kfnifv6+fyR/fzRo69hDeznbc5pmB6An/97eP5L0P8s3PNfVvU7PHl+iju6qvmNOzr40lN9/PCNCf6gbVC6Ofb8PCyMw3d+T/Zmqd+b97iXphaZWQxzz85aWquc7G4o55mLMxyteVPmdG8/JFdj9TdC7xN5pcGl8vqIh3A0zl07pHB+a1c1PA6v9g7zjrFXl10yZXVQu0cqgVU+A+DVIQ97G104iqWgb6tyUl1azIW+AZgfgAMpQcamW8Bml37nNSiBvulFgpE4N2Wsxvc1S8EcH3sNOgwyRZoPFrwKf33ES01ZCQ2u7NqBm1vc7NUG5Q8NNxoPoAur4RcLVgJnx3wIATc2r7CK9Y3hjPl4LdLKgTk/22pWsAZsxdB0s1QCG8Sbo16EkIqzIIZfkAVuNbtWfWuFo4gP39nB3z3ZyxsjXm40UOybTaGt7dzAXMrPaZEiIcQjKe6ebkBfEnVrmnZI0zRDB62maUc1TXtZ07SXp6en1zSx/bX7uan2JvZU76HT3UlLeQt1zjp+eiGAq8TJ137nDsKxOD/rnZEfUoAjX4Xicjj33VU969neGW5pdfPA/ibKS2w8dXFalsED7HinzNEePAVBX95jjsz7uTyzxL07a6krt7OrvpwXB+ag/6RcMbXfIStDQQrRVZAM7HXKP9fBjkpeHfYQH3pBCkp9Vd5+u3RlxDM70eTmlWE9+CaDXzc2V1Bk1Rg//wIg0jMqWm+VzxArp3emEosL3hj1pn2gNU3jlrZKIkMJQZK6MraVQP0NMPH6qp6jc358AYA9ja604zc0uSjHj31pBBr2Zd/Y3A1L0+AdXtNzAd4Y9Zi6XyqcRdxROkpEK5KBSiNqd4HNARNvrHkOOm+OSqtk30pKYPJNAM7F23gjcc+KNB+UjeZixkV3hfJq4v8yU5GvmpGXoOXAmttf/8e3dVLpLOKhH50vbB7rxKb0N024jR7XXUVCiM8mLIHqhMsojYTyOCiEOFhbW+CuPxk83z/L3TtqubnVTbndxqneWbj8U7nqrWiWwnUVWQoLwQivj3q5Y3sNRVYLt7RX0jM4L/9RqndAeb3MfEDAWM+K4+m8nnABdLdLQXqwQ44rRk/LMvUiB1S2g6tFBqlWwWsjXmrKipOBvQPtlSyGogQGX06Y5YkimuaDEFmC6QurG3/YQ3u1k6pSWUlpL7Kyp9GFNv6KvCC1cKjpFgh65Mp9FVyeWcIfjmWtSPc1u6haTMw3s5y/bq8s8FmlwgE4N+6j2GqhszZ9Ret2FnO3a1L+UG+kBBIKdWRtLqGlUJTeqcWcK++bi4a5RJt5HYDFKl16k4UrgTdGfdSUlVDvWqHZW0Lh9Fk7eGPEuOdRFo37IRqE2d4CZ2nMa8Me2qqW/y/XRNAHk2fW5ArSKbcX8fv37eBnvTP89NLaFrnrSaFKwAPo6QhuYNbkukN60FjTtMOJeACJ6wvs4pQ/M4shRj0Bbm51Y7Vo3NZRxemBGfkBbb9dXtRyUAq9YH6rl3PjCwgBN7fKD2l3m5sLkwvER3uWg5JrEASvjXgotlrY3SBXnre0VuIPRxDjr6cLt8abYHx1q9szYz72Ni2vLPe3uNGIUzz1RrqA1uc/9sqqxr8wscCehvQV8876cqp956XSSg3MNt4sX8dfXdUzeqfkynxXQ3na8V315WzXRgmXNUNJ+jnq90FgDhYnV/UskMHZHfVlFBn0hc+pBOr3gaVIrnDXwIXJBeJCWhyGCEFbuI9XI214/TkSFRr2rVkBpnJ23McNTa6VA6uTb4K7nbbGhvwtAd2dtQ4WixFvjK6D+2X0NFnW7Br4D29to9nt4KEfnSceL+xvUiiFKoFHWRbincAJAE3TkvZWIgNIVwCHkLEBPR7QxbKLaMN5PbEi0V0INzS5iM1elqtd/R+w+QBy1Z6fUDoz5k2MJf+59rdUUCPmsSxOLAs4RyVUda1KEJwd87GroTy5Nd3uxnK2aRNYIkvSd6rTuF+unEKLJiOlE47G6Z1aSBMqHdWldNlmKIr50wVZ5TawFsNM/pZAOBpncM7P9rqytOM768tojg0TqcpwWdTuBjSYvpj3MwAuTcrft6s2/Tk76svZqY0w5zCoPK2/Qb5OnlnVs0Aq+0xXkM6NtmHmRRkLxQZWq61Y+uFnVvf76fQmfs+d9eXGF/hGsUe9nBUdXEwoRkMKUIA60VicvqnFLMVryOQZqN/Hjc0uzoz6EPkon5qd0tU5sTaFmQtfMMLIfIC9Jn/DvBl+EdDMg/B5UmKz8vF37uTNUR/ff2N85Rs2kIKUgO7eSQh3T0pm0BMpxx/SNK1P07T5lHs+mLAG+lKziTaaCxPyA7W7Uf4T72l0sUsbkid14ae/Tufnrzs37qO6tJi6cmke76wvZ4dlNDFWSrC2bk/eY4IUcqkf/O11ZeywJP5ZalOydRpuBETeLpvLM0tEYoLdKR9kq0XjbZWzy/NMnrBJ5TVzKe95D8wuEYuLLCWwo66ULm2cGUdGxW6xE9ytqxaSl6YWaXY7ZKVuCh2VJXRpYwxa27JvWqMSmF4IMbMYMlUCreF+zsfbuDhloohrd63qb59K7/QixTaLYY8eACbPAnA+3sqFiVxKIPG7T7y5pnkADM75Ccfi5gpJJxKQC5OGfexqcLEQijLmDea+B6Qbsm7PhlgCFyf0mE4eCiwXIy/JOdoLD+j+ws3N7G4o53M/Pk8wsrq423pScEwg4b8/kZrvL4Q4kHg9IYSoFEJ0JV5PpNzzTaO6go1kYGaJmrJiXInGUXsaXey2DCHQloVfWZ3ML586l9eYl2eW2F5XljSPm90Odtlkh0Wqty9fWLsbZvsgGjIYJR1fMMKEL8iO+mVBWmKzcqAsIairUzxo+jPm+vKeL5CVrdHtSMy5NiPjoXbnqgR0b0IQZiqBPaWLOLUQg1pL9k01q3sGSCWQ+v7o2HxD2LUIZyIGKYzOKihvXLUSuDiZECBGK2AhKF+4xHnRSt/0kvEAtbtlzCOShyDM4NLkAl21ZVjNUiwT79t4cXtynoYkFeDalYAuSHcavO9pTJ2VWWb1+5KLjYu5FFQqjfule7NAt1Um5xLP391QgCUghHQHrSGd2QirReNPH9jL8FyAR57pX5cx18KVu/HlBnB5domO6mXh11LpoEsbx1vSuFzWryUUQp4r64FZf9qYmqZxU+ksYYqhvGn5wtrdsuFUHkEvXZDuyBCku4un8Wgu6V7SqeyQfWryDKYNzEpB1ZGhBLq0USZEJQFLxge8Zqfs7hjNr33EpclFNC3bTVMfkhbX2XB99k01O+X84/lVQcfigr7pReMVaeLv9vyCSUJB3V6YWp0SGJrzA9BulOa4MI4l4mdAa6LfVAnskkJxDQHP3unFLIWaxsxFcFZTX9+Y2xJwVMr+PGtwhelcnDRW8Fno1kbDPnbWyb/RhVwKKpWG/dJt5ctd47Nazo37cNltNFZkp9nmjWdQzi2fCug8uXN7De+9sZEvnuxlOPF/ttlcV0pgYGYpbQVss1rYUTTFuLUp/cKaHXmtTJdCUaYXQrTXpJvqXdZJhrWG9BQyPT977vKK4w7NJoROdbrQaWeM/nhDeiDJVgIVLdLKyIOBmSWqS5etIZ36yBgDoiEp8JLU7JLKay6/lUrvtHTT6Ln7OtqsdCm9sGDQb6ZmB0T84BvN6xlDc37C0bixMEq4XU75algIGgRKa3bAbP+qVppDc36KrJphnr7+vgfKt9E3beIO0vPJV+kS8oejjMwHshYDacxcgpqd7Kwv5+LkQm7fe81OmM3ftZfJxakFWqscOItXKC+aPAPFZeDuoMJZRIPLnr8lkAwOry2V14zz4z52N+YR0M7FaMJz3bR+SgDgvz6wB6tF4y++f3Zdx82X60YJLIWiTC2E0lfAQtAmxumLZ1QQutvBPyN7hudgMCGsOzKEdXNslEuxBiKxlJVtZYd8zSMVctQjd5tqdqf3N6kNj9Ifb2BqIcOlVNW1KndQphUAUB4cYShel7QUktQkArl5Bod7p0xWrjMXCVjKOD1jkJ5XszN5Tb7PAJMV6cxFgo56FnEm/z5pVHXJRIBVBEiH5/w0ux3GLpnE6t5Ss51+MyVQvV1aa6tMte2fXkKIbIswjZkLULODHfXlzPsjzCzmsNhqdkilsUZXy8WJBXatFA9IzmlnchG0s6Gc8/kqgfobAG1d4wLxuODCxELhQeGxHhm41l1r60RjhYM/uG8Hj5+d5MTZtQfu18p1owQMfeFLMziFnzPBDNeBLrA9QznHHEwIzPbqFEsgFqUiOMrleD3jnhQfsKMSSlx5KYExT4BKZ1H6ajq0iDM0RX+8IfncJNVdea9uBzJcYgCE/RT5pxgU9dljJ5XAygJaCMHlmUU6a4yFs7e0g5mlMIFwRhAsqQTyW6XqZnO7UbDUM0SsQgafjZVAIp6Sp2UDMDwfMA/MzvaCzU5l4zYGZ/3pil+nyC4zrVZpCeRUdgBLs7KHTc0uuhL1C/r/uSHVOyC8CAsTq5oHyLYZMv6VjxLoXf6/AXY3lNM7vUjU6L3JpKRc/o3WmFJrxMh8gKVwLC0ZYk2MvpJeR7OO/PZd29jdUM7/96038PhX17m3UK4bJZD0hacKwEQVZ2+4Mj3H2p3IYFlBCQwYuW28w1hFlMuZrhVNk8VdnsEV5zruDdJYkdHlMCG0BkQDg5kum6ouCHmlQMiBPxxl0hdiW4b7Sp/TXHFj8ndKUlwqfcl5uJvmlsIEI3HjDo1zl4m4Zdrm8HzGM0prZbZFnq6KkfkA9iKLcdGPZ5ji6oQSmDMQiPqmJatQAiNzfloqTZTAXD9UddJV5yIaF+Z+3equvFyBqQzO+mWX5WozBZR4v2p2Jhc3A7mUQM329PtWwch8gGhcJJWNKeEl8I2kVS/vrC9Ppg7nRf3evBMz8uHsuKzU312IJRCPyVqWdYwHpFJss/D5IzcxtxTmz7+3uW6h60cJzOgB0ZQPVCL4NCaq0wW2O5FeOJ9bYA/OLlFTVpLW410Xlpfjjdn+dXd73pZAkztTCchxB7UmY0sg5dlmDMwk3FeZ7qDEnKIV7dljg3w/PCu3PRhLWD7NmUogFgXfGEXVHcByzCOJpknrK8+q4VGPFMpZ/t1YFHyjFFV3UFNWzOCMgdBxt8supnnGUJZCUWaXwuZtk2d7oborWUlsmiFUuQ3mL686FtHoslNiM9mVS7fOanbQ7HZgs2j0r2QJwKpSfnUGTLLKstCVa0qPIt2FlHdcoHaPfK/WkE1lxPkJH5qWR1ZTLmYuSStqneMBqexrruD379vOt14Z5cdnVm+trZXrRgkMzvqpKy9JD2ollMCEqEpfNZbVyV4rK6zapWslY5U2L1d7Y5b6bCVQ2SGtixWyYMY8AZrdGUHIhICMVbRnuzmq9KBzbsE2aGQNQXKFWlzTmVQUabjbVrSKQApnyI5lsDAOIkZZXQdA9vsCUjjn8QyQq9KsZ4AMLIsYuNtoq3IaWwJWm/x98rQEdKulzcgdFI8l9sXtojMhHA2VKEgLJLwoW1nnydDckrkbCqQisxSBuw2b1UJblTO3JeBqlv/Xa8hS6p8xzirLQlcwKe6gHfVlaBr5xwXqdstsqjUW2GVyfnyBjurSlQPaudBbvmyQJaDze2/fzg1NLj71b28wkU9txTpw3SiBCV+QxkzB4RtFWIuZozxdsGpaQvDlVgJDs/5s4eAbA4sNu7sx2+1R2SF7o+QISi6GoviC0ey5ekfAXkFtdbWBhdEqX1dYresB5yx3zfwAFJdTU9fEmDdAKJrhs3e3SQG7QmOvUd0SyJq7nFdp3TZKi60mSiChaPJYKY96AsYuJ12JuNtory7Ntjh0qrryVwJz8j1rNXIHeYYgHoHqLiocRZTbbca/G0hLAJKLhHwYmjP4/0plfkC+b4l22dtqSrMD+6lYLDJIvUZLoNxuo3qlvju6gqlatgTsRVY6qktzp7CmohdDrrHALpPzE77Ci8RGe2TGU2rtzwZQZLXwP3/5FoKRGB/9xiv5xVEK5PpRAt4gjZkpfr4xtPJGqsvs2b5cd1tOd1AsLphcCGW7bXyjUN5Ec3V59pjJgLP5uOMJQZ01rncUXC20VzuzBY2tBErrpC82B+PeII4ia3JTlCTzA1DVQWt1KUIsu3WSuNvkCnuF8cc8ARxFVtzOjPG98j6topXWKqex3zwPBQlSSXr8kWyXEyx36qxopa3KybgvmK3QQAYe5/ILpOtzNVyR6+6rym1omkZblcHfJvlMPRaRnxIIRmJM+kIrKIHLaRuzdySUQM5eNDXb1xQTGJiV6dUrpljO9sr+UMXp895eV2aeQptJ9XbpsluHuMBSKMrgnL+wIjGQlkDjzcv7U2wg2+vK+Mwv7CMcjeMLbkxH1VSuKyXQkFko4hsFVzONFQ7GM02vytzuiZnFELG4yB7TOwquJtqqHMYxAcjp+9ZX601Zcx2BihYaKxx4/JHsDJuKZvnsHIx7AzS67dkf5PkBcLfTlHBB6Ypoed6JGMkK7prR+QBNRuPr91W0mAvK5HuT2/oandetGZOVORpUSGUpxPJKPo1VuGaG5vyUFlupzFRsyech/1eQ1oJpYNjdLueWpyWgj2MaFBYC5gaWLQykEghG4kz4crgRqnfIeedRuZ5K/7RBVpkRM5eWA9ApdNWWMTC7lN/K1lYsLYl1sAQuTMoGjwVlBkXDMmW1+ZaVr10nPnCghW9+5PbCOp7myXWhBBZDURZCURMl0ERDhZ3JzA+Ou122ODbpJqorjawKRJ/cI7XJLYW1P5yiyfMQpvq4hpZARXNSUI95M4RbRUtyxW3GmCdIU2bWkRDyPndb0o0zukYlMOYN0GwknL0j4KyGYidtVU6G5/3ZRU2V+WVkmcYd9HvLG8FWkkzbHTKKC+i/j3flGMTIvJ/WKoMgNEiLTrMmK8Pbqp0MzweMV+JFdnA15W0J6IrS1BIIzMuMMN26BLZV55MhtEP621eRHRWMxBjzBlYOCguRCJRn72vQVVtKJCYYnjdQykbU7V4XS8BsH4hVMXUGYuENDQobYTPoWLsRXBdKQA+wpFV8CiH9964mGivs2ZZARaLHjcnqeiIhhNMUS3LM5uSz0oI7RXZw1uQU1mOeABaNZEM6AMJ+Wa6esFqA9BoEkCa4bzSni2PME8hWWkGPLJ5yNSd/l6z3wtUCaHlZAlkBbZBumgoZt2irdhKMxJnOLHir0OMaAzmfMTKv++hNlEBCwOvuG0NLoCK/GIp+v2lw1jMk/08Sffxbq5yEo/HsYj4dPUMoD/QYlakS0MdJcQdt02sFcsUFdJ/2KuICw3N+hMgjM2hpGkK+tKCwTlei1sG0oC6T2j2Jfkt5Kg0Tzk/4KCuxFbax/OjmBIW3iutCCeir/DSB7Z+V2t3VTL3LjjeQ4WJxJTa7NulhovvN0/L5l2bk1o8VLclnZZnmK6zYxzxBGlz29FWA3k6hojW5kje0BMKLUqgbEI7GmV4MGQSc9bGbKbFZqSkrYSzTErAVy1VsDiUQjMSYXQobr9C9I0mlqp8fyXxGsVPGNfJwBxVbLdSUGWxq4hlMBslry0qwF1mM3TN5WjZCCIbn/cZBYZBz1cdiWWBnJQToVHWsyhIoK7GZuwOS8YiO5CGZTmrhslmaKiwL6FXEBS6vNjPIYAvLrkQBYd5xgbrdgCg4Q+j8+AK7G8oLaxcx1gOOqmWX5TXGdaEExo0sAd+y8Gs0EtiuRD8hk2DohC9Iic2S7ivWr3U1JZVDVppXRUvOHjljnoBxZlBirvUVJSbjJpSWieUy6QsiBNkrdX0uLl1I27PdQbBioHzMLKAthFxxJ1bfekB31MgtkEcx3ch8gOZKR/bG5YlaBF0oa5pGS6XTWCA73LJ6e4UtH2eXwvjDMfMaAc/QshuLZevENCupchssTeW198PQXA43FCwrkxQlYLFotFc7c2cIlZRDWf2q3EHJavuVYgK6YjFwB1U4i6gpK6ZvKncrliR6htDU2uMCQgjOTfiSrePXzOgr0gooRJFcwVwXSsDQEtBX+K6mpHIYT11dlzfIfi8mloCs6s0IgibHbE4Z08QSMHHbjHkNCsV0JeDSV+vF6XOFpBA3UzDLMQzj9E1diRgGyUEK8RwWzKiZEgjMS3dTYoVuGneAvOoRRjwmNQIL4xCPpq3MWyodSffRWp41nMsvHwnA4kTa6rC50oGmmdRBwLLrJo+iOJkemsOFMX9ZWk7F6YJ5W01p7tYRILOjZvNXAgOzS1SVFlNhFBxPZbZX9tbR3W0ZdNauJkOoS9ZATK89LjDqCbAQjBaWGRReknPY5HjAZnJdKIFxbwC3swh7UUp6V3IFvOwLT1tdW4vkislEqE54A8aZQQAVLTiKZapk1ord1Zxw22QHnONxwbg3aJAZpM9VWieNFY7sNM5kDMN4dasrjaZMS8A7KtPxyuoT5x2MeQLZgVt3q5yHyabzYyZN75aVjJxfub2ICkeRsSVQ0Srnk6OYbnTev2KNgE7ObJ2K1hVjAnoQ0zAmoCvEFCVQYrPS6LKbu4PyrBWIJ9pPZHaRTWN+MC0eoNNRU8rQnJ9YrjTRVdRJQKLpoFmWUiozvQnhbSxWumpLc1c0p2ItkvGLAiyB5aBwAZbA+OsykH6NxgPgOlECE95QdhvgRFEXpbXm/ntXk6l7xbC/j29Erl6ccg/dBleOgLOBcpldChOOxo0tgbJ6WQ8AiUB2hhAtq5O/j8l8DWMY+jzKm5L5z01uO/5wDG8gow1zRYusFTBpPjY6LwPa2YpRd2Utrw6b3Q5GjASlu1UWXy0aPyMYiTGzaBJ3SKahpiiBKge+YDT7d4G8itN0BWKodHTXWIrSkc/MoXjyrBWYWggRisZzVwvPXU5LD9XpqJZZOFn/H5nzWJzIe0vSyzNLbDNqCpjJ7KWcxVRdtWXMLYWZW8qzQVrd7oIsgfMTsmfQrkIsgbGNaR99JXF9KAGfwardNybTCS1WnMU2XHab8ardwB0UjwsmfUZ1BzLbSF8JNVTYmfAZBHDB0LWif3CzMni8I8uBauRqPSs7yGKVzzZ1BwVw2W1Z2zHqqaepY4NBwZguxE0sjVFPkHqXPXsjds9yAZdOc6XD2B2kC3CTFbru2mkxcpNkWBywXEtgGhwOL5gG0vX7asqKjdsN6LGLyvRgYc6CMUel3LVuBUtgxfTQaEj+nVPiATp6Z1XDDqo6yb0tVrYGTJsOZhKLSDeXQWaQjr7R0OoyhAZldtwaODe+QFuVM72312oZ7ZGfvXKDzZCuEa4PJeANmQjW5c1kDH3hJkpgdilMJCYMxhxNE0KNFXYmvJmpkOZKwDS46ksX1I0VdhZC0exNU1zmmUdjnmD2uCCtF5eREshfeenXG47vHQabHUprkoea3Q5G501cTvo9Bizvs2BUKDYIZQ0yDTeBntVjGBdIttowjwsMJ2oEDPEMgrVYPjOF1ionk76Q+Z6xle0rZkAldzLLlZqKMHQH6buf5QwOV+WvBEybDmYyPyhjMitYAoD5DmyZJDOEVrcPg865CV/h7aPHeqBp84rEtoJrXgmEo3FmFkPUG7mDUpSAYcGYqymxWvSlHV5esRu4g1LHdDmYWbtsxJoAACAASURBVAwRjqb4uMvqE24bIyVg0HtHiIRyWV5J69lDhplHOYR0ltKKx+X7kGoJVOQoRoOcAtpUCVS0pGVWtFQ6WDJ0OeUWzMvVwrlrBHT0rB5j11NuqwMSNQJm6aGeITnfDP+3vno3fCYkmgiu1JNqCYtmsBjQMcgM0ml02Sm2WcwzlCDFLbVyJ1WzPamzyJEZpNNc6aDYZsk/OFy7W76ucjMegEA4xsDMUmHtowPzUlFew/EAWAcloGnaYU3TDmma9ol8z690z3oytWBQ2ZtS1KVj6L9Ppommu1gMq4XjcfCNp4+ZSOdMUy4Wq3RDGbhtxjyyT35a7x09u8aVbgkAjBmlifrGDAOr40ZZR/6ZRK3EsvVSU1ZCkVXLdgeVlEtXhoGSkQFtk6wd70hWtkiyViBzhV5SJl0mJopmZN6PzaJlK3RIKIH051Q4iigvsRm7gypy1wpEY3HGPAHz9NCMGgEd/XrDIjVY7paaI/g9NOensUIKTONnD8hXg5iAxSJ7GOWVJppHhpDhPhxG6I3jDGoEdKwWjW3VpfkrgarORIbQ6oPDl6YWiAvYW0hQeOwV+XoNxwOgQCWgaVo3gBDiBODRf851fqV71ht9tZwmOALzEA1kCGw7M4uh9J2hTIK4yQrkVCWwNC2DminuoAa9ViDPgrFxr3TZpKedLtcz6OhKIKvHj6tZzmFpKu1wIBxj3h8xTz1NGdti0WiosGe7g8A0TVS+b8KkWngk7T2BZV+9oZsmR9bOqEf2Psra5jEek9ZShlDWNI1mszRRZxUUlebIpgoSjYvclkBldvFQ60oFY5XtUvEujBufBwbn/Om71WUyfxmKnDIZwID2KpOtNVPJM0Po8swSdeUl2bGkTGYuydYgzqqcl3XVlZrvuZCJniG0BktAzwwqKD00uaewcgfl4kFAj6z1A4fyOL/SPeuKYX58So2ATmOFHSFIL/lPWgLpcYFxb5Biq4UqZ0o1Z0Yapz5m6hyWx202FKajnkB2bx892ydltV7vsqNpRpaA7lNPH9s04JySJptKU4XDOLukosVQQOvVv1mdPSOJrqCZloBeMGZWK2BqCZjVCExI5We4MjcpGNM0aTmYWAI59xEILUoryuB5OSuVIa9OssMrtZCeuyzHMSleaq8uZXDWoD9TKlWdebuDVnQFgWnPoEy6assYmvOnu0hzUbtrTZbA2XEfjiJr7vdxJcZekcrS4V77GFcBhSoBNzCX8nN1HudXumddSRaKpVULLxd16dQnawVSBFNZA6BlpV1OeAPUV5SkV60ajKlbCpOGVcPZbhvpsjER1Cmr9SKrhbrykmxLQL/G1H1l1jIifaWuB26zMLFgcga0IctNU+kswlFkNa8V8Awbpm7K3kRm3UMxVgKVTobnDILQ+vUmSmBE30fAsEYgoaQM2gjolcqmGULuDvlqEhxeCkWZWQznTg+dHzB0Bel01DgJRGLZ/ZlSqe6UCnqFNNGB1SgBg+6hmXTWlhKLC+PGfkbU7pZKb5U9hM5P+NjVUJ5dWb4aRnuu+XgAXKGBYU3Tjmqa9rKmaS9PT08XNJbeQ9/lSN1RLM9Vu61YmtwGQrXRlSnwspVAeYmN0mKrca1AhttGbzyWHWwek50qy9JT1EyzmSBLaS0LaYP21Da7NONTx3bbmVwIZRccuVtl58qMQjddmGe7m7LTNmHZTaN3BM16RmRJuuxSCEfjTC4EcxeKVWQrgZZKB4FEX6MsKnJbAlaLlm09QUqNgHEvmbYqZ46YQCuypfSA4elkZlCuFtLzA4ZBYR29yCxrv+hUqjrlaw6XkC8YYXYpvHJmUNAnFUoeG67oGUK9ebeP2IXMEMq/15EQgvMTC4UViS1MwMLYNR8PgMKVgAfQnYBuIHOnc6PzK92DEOIRIcRBIcTB2tragiY4kcjnz2rvoFnSBKsu1POpFRj3Bmk0WrFbi9MEqqZp1OesFVgW1su9fYyKuRqzNrNoctuzM3gclXL7QBNLwGzvg0y3QpPbQSwukkH1XPMGqWTK7TZcduPNZIzaCDS7zWoFjDOExr0B+f4YbiajWwLZz2mtypUm2pZoF+7LOiWDs3bjdr4Z+whkPbPSkei8aWB92EoSzfiMLYEVawQWJ2U8yyA9VEev7s0vTdTcJZTcl7uAnkGZdOppojMblyE06Qvh8UcKax99jXcOTaVQJfAokFhS0AmcANA0zZ3jvOE9G8WEN2hcLVzWkGwBDOBy2HAUGazaXU1pSkAIYbJBjV58lv6WGrapTq7Yl33f+mrdULmkWCzL48qCsTRBo2mJzWWyYwI1ZcXZG5b7RrNW6cByp9Isd5NxzGHUEzSp4h0GtKyYAyQKxnLl72fEBUZWSg8trYOi7HPL2TomVofBs/TrTQWxZ1Aq21LjBUprlZOFkEmlMkgLwsQdlLNfEaSkh5orgSa3A6tFM9/vGPKyBPT00M7albqHJjKDchSK6ZSV2Kh3leTfSK56u7SEVxEXODculXpBQeGxHvnchv1rH+MqoSAlIIToAdA07RDg0X8GnjA7n+OeDcFYYI9kCVZN0xLFXUaWwPLKd24pTDgWN9yq0kjYNbgcxvn8kDbumNfMpZJeKKbTWGEnEDHItc+YL0ghbZzDn52+mToH8/5E6av0UbOmbt4R2YjPlt0OuaXSwbw/wlIoY/s8k6rhZI2AWUzAIB4gn5MjW0d35xgEu4fnc9QI6Hv7mgRmc+5lAImCsQHDU4Ozflx2G25n9nsmn21eI6BTZLXQUunInSFUUrZimujlmSU0LYdC0pntlZZ1DsWUSldtGb35ponaimXa6WqUQLJdRAHuoNEeqNuTtU3mtUjBMYGE6+aEEOKRlGMHVjifdWwjyNnewUCwNhj15KlolhtlJFwGy64VA7eN4YrdzlSmf91RKVP8UlbUusBNyw4yqGfQySmoM9w140aFYrGITFM0sAR0ayTLEihrkHnbGZaAebXwkOH4kKObqLMq8d5kWgJ+495EYFgjkJxyiY1KZ5F5Oqp+fwqBsAyqmreQHjR1BcFypbJ5mmiHfO8NtngcmvObbykJCeWhmSo9HT1DKCcrpIkOzCzRVOFIb7xoxOwlqVANlL0RXbVl9E8v5s5eSqV216rcQefHF2h2O7L30s4XIa6LSmGdKzIwvF7MLoWJxkX2jmLeUUPBmjPYmsjrnjAqFEvZpSyThgo7sbhgZjHlA69pWZk2Y56AzJopTvnAJesZjJULkK20XM2yOVhseYVt2OxuYVx2RzQQ0i67LLLKei8slkRTveV5LybcHquxNGDZrZPlEtK0RD1ChhLwBKhPVMOmEY8nt8c0w7SpW1mdDIxn+Of1al/TDJ35oZwbjOjKwzxDqB0QhhbIUD7poRUtKwrcjsS+AjkFbXXuNNG800NnevNyBelsrytjIRjNnb2USu1uqazy3Bf5/ISvsKDw/ID87F0H8QC4xpWAYVFXyJeowDVftadthq1flxB8hjn3/jm5o5ihOyi/WgHjrqTGefyQYgkYVQ2LeLITpy8YYTEUNWghvbxHgRFNuQK3GcoLDAK2unA2tQQSAVvDWoHsgrHR+YBxPGBxUhZf5VIClU5jS0BLrKgzlMBwLiWQ3NvXXAmU24uodBblqBVI3JvhEorFBSPzftqqcrWQHsjpCtJpq3KyEIwy7zeJS4CMCyxOQmgh65QQQraQXqlxXDwuFUkeQWGdZIbQatpHiNhyVXIOQtEYfdNLhccD4LrIDIJrXQnkrBEwUAJufdWekk6YUTA27g1is2hUp25vaJByqtNgVH8AWTuMGbpUDNJOdWrKSrBZNOOqYUi6hMbNWkgnawSMV+qNbgPXmD7vFCWw3NQtQ8ksTUvhbDJ+XblsT2G+r0B2YDhnC+kcK/OWRBDacAN4gyCt7ss3jAmskB6qI4vUzGICHfI1Yz/lcW+ASEzktgTmL+elBPSMntzBYT1DKLur6bw/gi8YXTkzaGEMIv6c7SIy2V6nbzW5iloByCsucGlykVhcFLab2GiP3Bynbu/ax7iKuLaVgNGqPcfqerknT+oOY+lKYMIrWyZbVygU02lK+r4NfPeLk0kTVyoBs1782eNaEz10TN1Xia0ux0w3k0nfUcxo3lnxBkhsLjOWdDfpQjyriCtZUGWsBCwWjcaKHPsK+Gflrk7IPj4TvmAyyJtGskbA+DkALVVOwjGTDeANtrQcnvPjKJI7uGU/z7iFdCY5N7Qpa5BCJsMS0H34phu4hBalcs2RHqqjr+BzxgWSGULZLqHLiRTOFd1Bev7+KtxB9a4SSout9E3lu8vYdhl4ziMucH5indpFNO7PO8ZxtXNtKwFfEGvWqt3cEmgwqhWwFcv0w4Ty0LeVTCOHJVDpLMJeZDGo7v3/2zvvIDfv885/f+hYLHaxi8X2XliWVeRSpChaxaKtyJJrKMv2uMSyRSe2cok9GV+SG1+SmUsyks65Sya+ieXkHN947OhsxzqXk06iCtUoir1v7w0LLBbbG4D3/njeH/ACeF/gBXZJcbG/zwxnifIWvMD7PL+n8wyhUcwthzCzFFK3BFQKxTiVLpUePwmzhqOpp0mWwDANz7ao3+SVhTYE5leSWyJHh8uMRfdvMjB4nAmD3zUKxZRo1wrUxs4R9D2GI1LGNQIcPvtXM0NoaRpYjM0VGAzQ9DLV+b46LYHq4hTWh8FA55tggXCBrRkY5kFcHVk41UV5YCxdrYB2mihv98zz+jWJNo7TrwQYY2gqzWDUpNlGn1mHJdA+NgOryaBvEpoa4RAwdhGo2p/+vTlCTiuBsekllDqtKqt2ltQHHoitltVrBbgS0BhQw4yqDb0YY7SqVgvgAsDMSFRBqCoBlUIxjmog21YIWJzR8x2ZWlTvvJnCX688l3RzBUaCdD2SmrqpDJNJpDpdrYC8j7QtpPNKNJUZbZdiuAxf0SusgaGpxdQ1ArbCtP1kamXrw5tYcBc9bn2SBTIQmIfFaEhW2BwurHW4XmxmGnWZsqW0NZ/uA5U00V7/PEwGFlWgmkx2A5Z8SgXOgGZPvn5LACCXkE5LYGu5U73ITw/+DnJvCSWQG6j72UfkrJBkU6/QrrFql6uGJUnSsARSC2ta8Wo3e4sOaddRz6CkwkV1DUmrTUXBmGbnzRSZO0DMctCeMEb7H9bKpw8OAtYCEpgaVBXZ5VGKidYGP8Zg9BiASjU1P06adEmuPNSrhnmQlgSyJEkYDqQYJjM1kNYKAGLxBE0h7EquFRjwL6C62J78XXG424av4NNQ53aktgT4vlTcQb2+OdS689ILU18HuYI0aia0aCrNx+j0UnKdiBaeraRwQtqjKSVJwo2xNQ6SGTlHfzdJUBjIcSWgWsSkkR4K8IIxO8aSWj9TAVZwYRXLoYjuGgFOhVprZkXWEV/Nq1oCGj57gGoKVsKR5L44ioKxEa2A6vRwyn1XRbOPtCwBEtBDAa3B77KwTCEc+DGSRmU6y2nwDrcEtCwlIGWNAMdmNqLUadUeM8nPF8D04ipml0Pqn4m/L008AFC2lE5RMJbghhoILKQOxE72kmvQqk/I1ZfoaCntblR1B/X559GoZ66wvwso2arrfJRkPmVsO00uS1HX4JtbxuT8ytpmCo+co4WLTkWbC+SsEghHqL2Dag/9NAI7uWq4Eliaxrh/MvqeODRqBDiVLjt8iSteSx71GZoexmiQhrSXKv3qKeoZlOcKqLhsFK0uhtU6by7NUJpjCndQWaGV2lUn7tvioFjC9DCWVsOYmF1WXzVr9NtXotlS2mCUU2iH5M+wAI/Tmly0FAnLx6lPeRyArAHVmIC9iCwW2RKI+uXVPpMkyUonvRKoctnBmIYLCkhqKS1JEgYm59PUCPRmJJzq3A5Mzq8kjyFVUtyUlCYajkjon1xAU7p2EctzZK1mEBTmNJfSvrt9yempqnhkRZMiLnB9lAo6d1SuMShcuS+p/Usuk7Of1DcrDzpRruj4TZxCaJQX2jTTLoPjfdH3xO1To6qXwxWRN3HesLxiH55aREWhPd70TlEolrjf5CpnyjxaWVqEd3YpOaAabU+trQSsJiNK8q3Jq3S+nay8ABVfvU5hyVtAaI5/lC2BgckF9Xm7s2OUhqpDCdQUp6oViGUIDUS7eKoIwDkvEFrSdTyLyYCKApu2EnDF1wr451awsBJOHdAM9MTSOnXA96UvQyi2wh6ZWsRKKJK+ZxBvHFeyRfc5cWqLHTAaWAY9hFoAsJRxgetyz6CsG8etLgLea5umSIyTs0qAtymuVloC8z4SrCmEU0WhShtlWcDP+4ai74kSHf+oLaw1WyTIhVeDgYXkFgXREYL1Kc8VUPHbyy4O/0gPJElFSKfo7qkkXcFYrKlbguCa91FwLY2vnrq7qlQNR49B11uzilZHMzVOTVEeTQtTFgJyFMPfB+SmaarH05kZxKnWGmjDj6nYJ8/nV1U+AK3U57zkvtEJLzpLqQR4kFmhBHrk9NC0mUH+7JWAxWRAnTtPf4aQJY+uWRpLoLpoDe0ixi5T5tsmCgoDOawEosFEpQCM3sTawqmi0J7c5kEW8CtTQzAaGDzKlFPe0CtF7rZ2pk0VMD2i3rFShxIodlhgNRmSLQF5m+BIJ4AERQjoSt8E5JbIWnn808OKytpEBaYvl95iMqC8wKZdNTw7hqWlJYzPLKmnTepopsapKabvNSmbCojN/ZUkDAQWUFZgjW/fwdFZI8BJOVfAXkS+Z/l75oJac44AF9IZWAJ1elpKcwU6GQsOcz992hoBXwdlxWXpP2/y5KM74wyh1EqgdS3to3mlsFACuUG0IZtSAOq4iVX97M4KAEAkOIIqV4LbJqMVu4rbZnkaC7NTyRk2XMClWHUyxlBTrDLFSr6xFyfoxk5yBwWHKPCqUX/AqXOTC2U1cfVcWA0sz8Dnm4DZyFDqTIiRBPWvmLWnmNUAUgTjw72QJA3hONVPnyONRQPoSBMNLQJzExiYnNdejQf6oKd5G6emKA/jM0vJtRac4qZonv3A5DwMTMWqih6bKwH9AtdhNcHjtKauGuZpooqq4T7/HApsJrgdaYql/J20+MmyqKq5NB/9k/Pq1pkanq1kfYSTM4rml0Pom5zHjkrtbLS0jJyj4tAM0103OjmrBEaCCyi0m5GvHJCtp7qUp/YphYXZBuSVwDQ/miyMAulXoza5+jTJJy27mSpYIHmlO9VP/eqtqU3yercD/f4EwZZfBphskAJ9YEylUCzQQ+erkdLKqXPTKECtWoFF30C0d30cwfQWF4cmjGnXCgRGSEiq9tMJ9NF3qZgLoUVNquH20ZbSA9rxB4B84IU1qnMLVI9ZnGKWMkABVXkFPhBYQKXLntwgL3rszNJDOfVuPRlCTXFpor2+eTR68tWL5ZT4u7JyBXGaPPlYDUvajfYS8WyniXxTfUkvtY/PQpKA1jUFhc9tungAkMtKQC01MjhAhUUpBGvUhE4QrFJhFRxL3uQUvqk+qihOUawEkLDuS1yRycqokk0mZ9jobBRW787DQGA+vlbAYACK6mGZHUSZU6Xz5qS+ACMXhklCRD7v8NSgeirlVPrrzKly2dV99fIx5ifohlf30evrowNQTYWBaVQNy668ZV83JmaXtccp6pyjy+HnrFkr4G6m7JqVBfRPLmi7ggCyBPLLdV3T+HPQ01K6IckdlDYoHA7J1yN7JdAi9xDq9OptJKedIcSDwlkrgYUAXeNN5goCclkJBBdV3CDpC4tsZiOqXPZo7xTOan41KiLe5Bt1akBXL5eGEkd0UlMUOU+/kvlV3EH9ugKedSUOLK2q9MUpqodzYTj5ZpYk+rHrqDrlwjDJnSALaMPMsHpe+1S/br95VRH56r2J519YDTADwpP9yLNo9PGZ6td17QEatFJRaNdwB9UDzIjZ4RsAUqSH+rt1zdHl8Fx4zeCn/B1IgR70++fT1Aj0ZOV7r3encUkBtCCYnwCWZzG/HML4zFL03DUJDtCqfA1KYEuZE4wBHeOZpIkywHs96aXro9Nw5ZmTCy71MnqB/gpLIHfYU+3CwYbi+CenBnS5KBpKHOhLWD1N2apRwyZQX5TwIwvoW402eBzwzS7H52znlyMCI2qNU/FCLrRCGTw6LQEgOfgnFdWjNDyGpsRV7eyY7q6PpU4rbGZD8koyvxSSOQ/loRF1YeHv1C0coplTiW4akxVw1SFvpge1xXnJronFIGVm6bQEAMqSUnUHmaxAUT1CXko/VF2Rz00AK7MZKYEihwXFDksKJUD59TPDNzC9uBpdGasS6MkoM4hTV5JZhhAP1KatEeCpmmtQAnaLEXXFeejwJs94VsXiIEXovZL0Eg8Kp3VhacFnCm+SQTJKclYJPHNsN756qCL2RCRMWTE6Vqj1JXnoS5h8NGqsgpWF0GyLVXgitEw59zpW7Lz6Ms7NZDRhyuhGszUY/+OdHqKZABm0DO5PsDLm8mrgwBJaXQnVxFHfcnolwBhDXbED/YkChDHMFzSimY2gKVFwLU2TotEpHFIGbD1b4V7qVxfKfsp8yqRxWU2qlM2SFpiDFH9QzYqJDlPXrwQAEqaaufDyyj44RBZIS5lGJfBCgNJus6rMpc/SNZFitc0tjMludHjpfWmrbifk1bgn83NSsq28AO1jOi0BACjfCYxfjXsqFI6gfXx2bZlBQ6cp5pCizUmukrNKAP+wF3jxz2KPgwNUWKRDaDSU5GMmYSBHd5iaw1WGY0PnKdAs6XJJcLdMb4KbaQQlqDNMxL85g9THSpcdZiNLEtQjjDJ/tln88RtEuz7qSzWsdedhMJAsxHzWBjQbRpJXjDx3XKdwqC3Og9nIVAeMhIqbUR0exbZSFSUwQYITpdt1HQeg4LB3ZlndNVLSgoKFQdQUWuC0qeSZR69bZkqgOVW3TGs+4KzE6kRX9L2qRD9r5v3tmzz5MLA0fnd3C7VqnmhH5/gsbGZD+rnC3mtkVdvWIHhBc4D7J+exuJLCXaWkfBfdH0sx66HPP4/lUAQ7qrI8l0gEGH4PqD2Y3fYbnNxVAs7K2M0DxMxXPqAiBQ1yL3ZlXODqIikBy5RiuhEXDDosAXJpxPdKWQlFcG2lAjVhylFPOlcdq2mjgdJEE/32nSFSAvUYjd8g0EO97AtS1whweHZJOKFJXS+qUMkCqLQltCTI4DoDVCvQWJKPThW/sNdSBytbxR6nirvA106ziHUWbgGKkZZq2TolW2CWVnHIrWEp+LvouulIR1XS5MnH5PwKphL7O0WP2wzrdDecNlN82xAlfNWdgcLj2MxG1Lsdqtc3itlGluHEdXR4Z9FS6tRuYqc8p7KdGZ9PItsrnIhIaSwVJWW7YseXuSa3i2ityHIV72snC7ZGKIHcoqyVlAAXrjyjwJNesDbIrps+hevmfMCCWUMBMHEt9kavbJbquDltZiOqi+xxweH+yXl0RiphD82Quc+ZuEHZNfmetPsFgAa3I2m1eWmuCEuSGa7ZhJF8kz1kuejsjdJS6sRyKJLkrrmyQq42Q+LIP38HYLRkJJy3lDujbggl3RIdY6tpPHmjiRukJDPo8cKtMbUCpVARWUb78/1JrwEg5eZuzrinTNrgsGc7PIt92OJRiXtwJm4A1sKUVempaCnLR2c6IVvWCkxcR6d3Flu03FKc1SVSimU7sjofJdzt1K43OFwuK4HxWFzg2ug0LSbSxTG0GDpNf4USyDFKt1OTNN4nx3uNrAMdPr/qIjssRgO6ZMG0Go6gwzuHSUdLfGaC9zoJO50mcUNJvGug0zuLTklekcdZLe0Zrfq2VTjR65uPa1DXM7mIYVMtmD8hnc57TfcqHSBzHUi+SU/PumPnqsTXScJSR+5+9PzLnRieWsRcQlvhCwtkfZWvDCRvNHEj45XxtvICGFis0ZiSISOt8LebxtQ3Hr9M06YyJK0SKN8Jm7SEg64UQpB/1iyDnlvLnOj3z6fOECpthRTow8zMNLaWp2sX0UHtFdZh/GJtcR5sZoP+uEBBJVVbK5TApaFptFYUwJztDIGh01STs4k6hypZsxJgjB1jjB1ljH1b4/Xj8r+nFM89xV9b6/E1KZdvWJ76NXwWqNaXA2w2GrC9wolLwxQE7p6Yw0o4grBnO92QvGLRezWj1VBrRQE6vbNRYX11ZAbdTF4xj12iv+EQKZcMbrBt5QUIRSR0Kfy+HeOzCDiaSOhzFoMUG8lAmLWU5Uf3x1lYCeHMTCFCzEwCQYm/I+OMEb7y7EqwBi5PGjDFXDBOdsZvsDgFzI1npMwAykZpKHFEc8qVdMyY4ZMKUbPan7zhrJf69vBVaAZUFdlhNxtxQ0PIBZ10re6wDqu+DkkCfDeA0sw+q5KWMnK5pGzbXNoKBgnNbDS9JcAXQuvgDjIaGLaWOfVnCDFGx5WVQCgcwZWRaeytST3kJyWD75IVkG1m0QZnTUqAMbYPACRJOgEgyB8rXj8K4IQkSc8CaJQfA8BxxlgPAO3m4GulYg9gsgEDp4B5PwWTqg/o3nxPjQtXR2YQjki4NETKwNF0FzWL814F5icpQ6W6Tf8+qwuxGpaiAuHi0BTKK2oowMaHWUxcp2NkcK68QIavcL0zSxibXkKkfA9l6vCRmtx9Vb5H977zLCY0lDhwdXQ6+tzVkRmEJCMWCxvjlczSNKXMZugm2CoLnc4EJdAxPosJe2NSNggmZOsji5Voa2WhqiXQ6Z3D5UgjXFPJ6YfRVWd55paA0cCwo7IAV0emVV+/vFKJsMSwzTCovoM5Lym9Nay6uVBPKWjl/W8zDKbPsvFepfjIOq2ct5Y79dcKAPQ9TFwHwiF0eGexuBrGHbVZKoG5CZINm9QVBKzdEngMAM+Z7AVwNOH1RsVzvfJjAHhUkqQmWXncHExWoKoN6H8D6H6Fnqu9S/fm++uKMLccwuXhIN7s9qPUaUXZzvvoxYF3gMF36P91d+ve5x55tXJuYAqr4QiuDMsrmKr9ZKlIEjB8UkQ4TAAAEhpJREFUht6cgXJpcDvgyjPj7EAAAHBRVlquFvnzDp+lv9z3WblX974B4I4aFy4OBaMps1wpmmvaSHnxuMvIeQBSxlWX1UV25FniV8vTC6sYCS5izr2LFE1IUUzGraYsfNKtFQUYCS5ieiE+oH1tdBpDti0wTHZSn3wl4/LxsrAEAGBnVSGujc4kBdcB4MLYMvqkCpQvdqtsiZglm+WxAYqFWE0GXBtJoQSKG7DCLNhnHUVp4ijSRPgg9gxcfqnYVl4A/9wKJhKHOWlRvpNaegd6or/1O2qKsjv4Jo8HAGtXAi4AAcVjt/JFSZKela0AANgH4Cz/vw4X0lnG2Fmfz6f2Fn1sf4RWcb/5Y+rTU6VfsN63pRRGA8P/uTiKt7r8ONJSAlZYTel07b8B2n9Ls3wzKC6pdNnR6HHgtfYJnO4NYH4ljMPNJUDDPdQ+wNcOdJ+gc82gCMpgYDhQX4zTffRVnOqZpGHbO++iFduArLD636IVn6NE974BYG+tC77Z5Wih1bmBKVQX2WFrOESrVF57MCJ/vRkqAYOBYVdVIc4PTkWf4//PbzhAlalehTUw/B5doxST0bSIWk0JLqGLQ0GslO2l+ozxy/EbjV2m2E+aucJa7KoqxOJqGL0qcYHLw0EMWxph9iVXwQKgRYHBBFRkpriVmI0GtFYW4PKwujUCADAY0cUa0GbpT72zmzCIfVc1xelSnp+SCtmSHb2Ai4NBFDssyZ1s9TL4Lt0jGS6McolbEhiW3UQvS5J0HgAkSXpatgLcChdRFFl5tEmS1Obx6MuQUWXPZwCzgypkD309o8yOwjwz7t9ain99px/Ti6v47J1ypfHezwIDbwOXfgrsfpQsjgz4cGs53u2dxHdf7oDNbMA9LR5gy0P04pl/Iatl+0cz9k8eaS7BwOQCOsZn8Uq7F0eaS2Cz5wGN9wKdL1I/+oFTQP2RjPYLAIcaSbe/2eXHajiCt7v9ONJcErOs+l6nvz2vUQpfFsLyzoZiXBudic6cPdMfgMnAULvnPnoDV2SSBAy9l5G7TAmfOnVlJFb0Nza9CO/MMgoa76QnePVo9A0XswoKc3ZrCDlJknBpeBrzxdspVrMQSN54+Az5wC1p8vbTsKfahauj06rWCEBjNU+vNKB+Rb1LZxRf+7oPYt9RSQH7yxousyQ82+i+Hj6Li0NB7K1xZV8pPPQeLeQyvI9zibRSURHYVf7jgjsIgPdmcAGY1NjNUUmSnpb3d4wxdkx+fhIxF9H6Yy8CvnEaOPZD4K5vZLz5X36sFW11RfgPD7TgQL38Mdu+AlTfSRbBkW9lvM8v3FUHo4HhwmAQX7qrnvrWF1QA2x4BzvyAVr13fCHj/T6yuwImA8Mnvvc2hgKLeGiXXC297WHyeT7/B9QuedejGe+7pTQfNcV2vHR9HKd7A5hdDuHeLR7KAipuBDpeIAE2+C6w5cMZ7x8gJRCOSDjVQz+hk50+7Klxwe6uoWvde5Le6O+iiuqGD2R1nJJ8KxpLHHi3NyZw+TF3bm2h+olRhRKYHqEeRRm4EhNp9OQjz2LElQQhNza9BP/cMoz1h+kJrug4kTAppCwVnpLd1YVYWAlr9u+/OjKNi5EmmCPLFIjW4ib03M+zmNBS6sTl4WD6NwPU/bZqH8JDZ9Dtm8s+KLwyT+62TVokxknr1FO4c9R4DgD3sTQCOAEAjDGXJElB+f/HFQrgKCg2wAPCTQC+n92p68RVk3YQuRbVRXn4+R8cjn/S7gK+8hK5DdK0YlajymXHc1+7Cx3jM/jEHQp3xsPfpRbQ9UfI55kh7nwrvnx3PX7wZh+2lTvxib1yTvnux4CTzwA3fk1+zywECmMMn9xbhX94tRtn+6fgdlhw/7ZSslZaPw68/ffAC9+mtMHWT2S8fwA42OCG02bCC1fHsbXciWujM/izh+SMmKYPAud/RIHnzhfpuZbslA0AHGpy41cXR7EajsBsNOCtLj+KHRYKiNYeBPrepCpSgwHof5M2qs9O6QAUHN5ZVYhzA1Nxz3OXV0Xr3cB5O7nrtj8Se4OvHViZWxclwONRl4aC0bRfJZeGg7gkyVXkI+e0YxA3aRD77upCvNI+AUmS9K3qq/aDnfoeLNJK9kpg8F1adDXck932OcKa3EHcvSML9yB/DOAVxfNPMcZ6GGNTim0+LVsDPYptNg6MZaUAOHtrXHjsQC2sJsU+nOXAI38H7PxU1vv904e249+OH8K/f/1wbPCN2Q783q+Bo38JfOYnWafBPX6kAVUuO+aWQ/iTB7fGhr4f+gZV7l75GbDld7J2m1hMBjy8qwK/vjyKP37uIkwGhod3y9bM7scoEHjxJ8C5H1JsR+dgFzU+uLUUc8shvNXlx3IojFc7JvCBlhIYDIyUy/wEMCYHZNt/S63C15gOeXdTCa6OTiO4EKscfrPTD6fNhB01HqDmACkBJYOn6G8GSQJaNLgdcFpNuKix2j7VMwlzSRNgc8Uy1dQYeo+sgHVOp9xdXYjA/Ir27IVEqttgiKxih6E/quAypu8kYDCvycrLBdYc3lezFCRJ2i//PQEgKWyfxroQZInRwKL++ziKG4Ej31zTvl15Frz0zXswGlyMb3SW7wGeeBXoehlo+/KajvHkB5vxq0ujODcwhS/fXR+bslW1D6g9DLz4p/T403+1puPcs8WDQrsZP31vEDNLqwgurOJT++SivZYPU8XzpeeolULXS8C+L2ZcKZzIkRY3/tsJ4I0uPz62pxKRiISTnT4cbnKTwq7/APDa35BbLU92PXa9TAHpdVh1GwwMdzYU4+3u5IropdUw3usL4HMHa4HpNmDwtPpOZscpNXP3p9d8PolwQX5hMKg9XU2JnOTxkGs4+5nCfW+QlZVmFkiuk7sVw4J1x2E1qXe69GwFDj+55pupuigPL33zHnz/C/vxnYcVefGMAb/7zxQrefjvgNaPrek4FpMBj9/dgJeue/FH/3YR28qdFOgGSAC3fgK48GPgZ79HFsi+L67peACwt6YIZQVW/PoS1Wyc6Q9gfGYJD+2UrZ2GewFIlB0GUCC/9yQppXVadd+71YOByYWkjrNn+6ewHIrgAy0lQOP9VPA3rVK81vs6/W28f13OR0lrRQHyLEac6VcJjquwZC/FqOTGYWt/dgdcnAJGL1LixCZHKAHBbUV1UR4e3FFOrhklhVXAx/8ROPCVdTnO1+5txGNtNTjc5Mbff+aO+IZpD3yHskV6XwMOPLGmHH2O0cDw8b1VeLWd5hj/6zv9cFiM+PAOec5z9QFqTnfpp/T42vNZB/K1uG8LteF4vSO+a+2b3T6YjQwHG9xAs5zzwWtrlPS+DuS5syqaS4fJaMD+uiKc7tWnBC4MBnEh0oTGFe3B8ynpfwuAtOnjAYBQAoJNis1sxFPHduMnTxxKDpS6aoEnzwBfOQF85Jl1O+ZXjzTAbGT42D++jReujuOrH2hEnkX2yBoMwP4vAT2vkgB+87tU01Fz57odv9adh4YSB17vjNXeSJKEV25MYH9dERxWE1l1BdUxiyT2RkoBbrh3za4xLQ41utHhndXuuKrgVO8kLkotsM8PU1uPTOl7g2JZGdQO5SpCCQgEajhKKFi7jgHQ0gIbvve5ffA4rXh0fzW+fn/CTIeDvw8U1gI//hSlpT741+segP1Qaxne6vLDJ4/zvDw8je6JOXxsj5ypxhjQ/ACt+pVV2kOnqV/Tlt9Z1/NRcqc8CVCPS+hkpw8BtyzAeQZXJvS8CtQdBkwqY0s3GUIJCAS3kAe2l+HEt+7FM4/uic8OAwCrE3j8BeDe/wh84ZeUGrvOPHagBqGIhB+90w8AePaNXuRbTbFMLIDSfpdnKDOKc/EngMkObPvIup8TZ3d1IWxmg2rwWsnE7BIuDQVRv+swtdjuO5nZgfzdNAuk5cE1nG3uIJSAQHA7UVgN3P/nQNP6B18Bam390T2VePbNXvz5L6/gt1fG8PiRhvgMm8b7yCI59T1yA816gcvPUVaQNU2H0TVgNRlxpNmDEzcm4ka7JvJaO8U0HmitpLqavjcyOxCvNdkilAAglIBAsOn4i4+2orHEgZ+cHsQ9Wzx48v6EkZkGI3DPn1AvqJNPAb96kooj7/6jm35uH2otxUhwMeWQmRM3JlBZaMP2CicFdqf6gSmVmRNadL5I8RYd88Y3A+vTBlAgEGwYSvKt+M0fHoF3dhmVhTb1Ct07Pk/C8vW/pccf+a+651KvhQ9uKwNjV3DiuhfbVVpaBxdWcLLDh88drKXz5imePa8AbY+nP8BCgIrwDv/hOp/5xkVYAgLBJsRkNKDKZddu0WAwAo/9GPj8L4CvvQHc+cQtOS+P04o7alz41aVRVZfQ8xdGsBKO4NE2ubjPs4067rb/X30HuP48EAkBOz65fie9wRFKQCAQqGMwUt1Ahf4hROvBZ++sRdfEXFyTP4DSWZ87O4ydVQXYUSmPiWWMmi/2nQSWdEwnu/ILakh4E2odNipCCQgEgtuKj+6phCvPjP91qj/u+VM9k7gxNhNr687Z9jAQXgG6X0694+kRagO/69imHSWphlACAoHgtsJmNuJzd9bixWvjuCLPYAiFI/ibF26gvMCG3+V9njg1B6kD7+Wfpd7x+R/R35vQ+2gjI5SAQCC47fj9+5pQkm/Fkz89jwuDU/hPv7yKqyMz+M8fbY11sOUYjBTI7vp/6j2PACC0Apz9IfViWuc22BsdoQQEAsFtR4HNjH/6/H4E5lfwyf/xDp47O4Qn72/GR3ZVqG+w70tU03DuR+qvX/05tQg/ePzmnfQGRaSICgSC25L9dUV45Vv34o0uP5pL81MPjymqo5YW732f2m84FC3VVxaAV/8LBbgb178Ke6MjLAGBQHDbUlpgw7H91fqmhx39C2B5Dnjtr+Off/u/AzMjwIN/e9Oa321kxBURCAS5Qel24MBXgbP/E7j8v+m5q78A3niGptPV3/3+nt9tinAHCQSC3OFDfwWMXwH+/Qngpe9Q59OaQzSMSKCKUAICgSB3MNuBLz4PnPkXYPQ8zUNue5yGBAlUEUpAIBDkFiYrcNfX3++z2DCsOSbAGDvGGDvKGPu2xutPyX+P691GIBAIBLeGNSkBxtg+AJAk6QSAIH+cwHHGWA+A3gy2EQgEAsEtYK2WwGMAgvL/ewEcVXnPo5IkNclCX+82AoFAILgFrFUJuAAoW/25Vd6zL8H1k3YbxthxxthZxthZn8+X+LJAIBAI1ombXicgSdLTshXgZozpWvVLkvSsJEltkiS1eTyem3yGAoFAsHlJmx2kDOgq6OU+fQDF8nMuAJMJ2x4DAEmSfi6/1phuG4FAIBDcOtIqAUmSnk3x8nMA2uT/NwI4AQCMMZckSUGQz79Xfr0JwPcBnFXbRiAQCAS3njW5gyRJOg8AspsnyB8DeEXx+qdli6BHkqTzKbYRCAQCwS2Gqc3xvJ1gjPkADGS5eQkA/zqeTq4hrk96xDVKjbg+6Xk/rlGdJEm6Aqq3vRJYC4yxs5IktaV/5+ZEXJ/0iGuUGnF90nO7XyPRRVQgEAg2MUIJCAQCwSYm15VAqswmgbg+ehDXKDXi+qTntr5GOR0TEAgEAkFqct0SEAgEAkEKhBLY5CR2cVVr/b3ZUblGohW6IC0b5XeS00pAbkR3nAs2+bkN8cXcCuSCvR8kPB3X+nuzk3iNRCt0bcQCIsZG+p3krBKQb94TctuLRlnwb5gv5lYgX4dAwtOJrb83NSrXSLRC10YsIGJsmN9JzioBUF8ifuF75ccb5ot5H0ls/S2IR0/79M2KWEDE2DC/k5xVAnI7ap6atQ/UuG7DfDHvF9m0/hYIZMQCYgOS84PmZZfPy5IknWeMvd+nc0tJ0wZc7f1qrb9zmkyvEUQrdE0kSXoaABhjH2KMHd3kFsGG+Z1saCWg8wY+yn+c2EBfzHqQpg24Gmqtv3OaLK6Ravv0zUCq+20zLiDSsGF+JxtaCaS7gRljxxWrk6PYQF/MrUC+cdsYY8ckSfq5bC0dZ4wFILf+fr/P8f1G4xq1bcZW6Gnut023gEjFRvqd5GzFsHzxfwaKARSDglYn5NVML4DGLFaBAoFAA/neCoDurafTvV9we5CzSkAgEAgE6cnZ7CCBQCAQpEcoAYFAINjECCUgEAgEmxihBAQCgWATI5SAQCAQbGKEEhAIBIJNjFACAoFAsIn5/36Y+gGywLSkAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/opt/anaconda3/lib/python3.5/site-packages/ipykernel_launcher.py:29: RuntimeWarning: invalid value encountered in double_scalars\n",
      "/opt/anaconda3/lib/python3.5/site-packages/ipykernel_launcher.py:30: RuntimeWarning: invalid value encountered in sqrt\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/opt/anaconda3/lib/python3.5/site-packages/ipykernel_launcher.py:45: RuntimeWarning: invalid value encountered in double_scalars\n",
      "/opt/anaconda3/lib/python3.5/site-packages/ipykernel_launcher.py:46: RuntimeWarning: invalid value encountered in double_scalars\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "%matplotlib inline\n",
    "import numpy as np\n",
    "import scipy.special as scpsp \n",
    "import matplotlib.pyplot as plt\n",
    "\n",
    "\n",
    "xvals = np.linspace(-20,1,500)\n",
    "ai,aip,bi,bip=scpsp.airy(xvals)\n",
    "m=np.sqrt(ai**2+bi**2)\n",
    "plt.plot(xvals,ai,label=\"Ai(x)\")\n",
    "\n",
    "plt.plot(xvals,bi,label=\"Bi(x)\")\n",
    "\n",
    "plt.plot(xvals,m,label=\"M(x)\")\n",
    "plt.legend()\n",
    "plt.savefig(\"figs/qI-1-05-airys.png\")\n",
    "plt.show()\n",
    "\n",
    "\n",
    "#######################################################################################\n",
    "\n",
    "xvals = np.linspace(-2,2,500)\n",
    "ai,aip,bi,bip = scpsp.airy(xvals)\n",
    "m = np.sqrt(ai**2+bi**2)\n",
    "theta = np.arctan(ai/bi)\n",
    "theta = np.array([t+ 3.1415926 if t<0  else t for t in theta])\n",
    "\n",
    "thetaapp0 = np.array([ np.pi/6.-.63134 * t for t in xvals])\n",
    "thetaappp = np.array([ .5*np.exp(-4/3.*t**(3/2)) for t in xvals])\n",
    "thetaappm = np.array([ np.pi/4 + 2./3. * np.sqrt(-t**3) for t in xvals])\n",
    "\n",
    "plt.title(\"$\\\\theta(x)$\")\n",
    "plt.plot(xvals,theta,label=\"$exacta$\")\n",
    "plt.plot(xvals,thetaapp0,label=\"$x \\\\approx 0$\" )\n",
    "plt.scatter(xvals,thetaappp,color=\"g\",marker=\"+\",label=\"$x\\\\rightarrow \\\\infty$\" )\n",
    "plt.scatter(xvals,thetaappm,color=\"g\",marker=\"*\",label=\"$x\\\\rightarrow -\\\\infty$\" )\n",
    "\n",
    "plt.legend()\n",
    "plt.savefig(\"figs/qI-1-05-theta-asymp.png\")\n",
    "plt.show()\n",
    "\n",
    "###########################################################################\n",
    "\n",
    "m0 = np.array([.71 +.1957*t for t in xvals])\n",
    "mp = np.array([ np.exp(2/3 *t**(3/2))/t**(1./4.)/np.sqrt(np.pi) for t in xvals])\n",
    "mm = np.array([1./(-t)**(1./4.)/np.sqrt(np.pi)  for t in xvals])\n",
    "\n",
    "plt.title(\"M(x)\")\n",
    "plt.plot(xvals,m,label=\"exacta\")\n",
    "plt.plot(xvals,m0,label=\"$x \\\\approx 0$\" )\n",
    "plt.scatter(xvals,mp,color=\"g\",marker=\"+\",label=\"$x\\\\rightarrow \\\\infty$\" )\n",
    "plt.scatter(xvals,mm,color=\"g\",marker=\"*\",label=\"$x\\\\rightarrow -\\\\infty$\" )\n",
    "\n",
    "plt.legend(loc=0)\n",
    "plt.savefig(\"figs/qI-1-05-masympt.png\")\n",
    "plt.show()\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2018-09-20T12:46:35.534604Z",
     "start_time": "2018-09-20T12:46:35.532056Z"
    }
   },
   "outputs": [],
   "source": [
    "## Coeficientes de transmisión"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2018-09-20T12:46:36.187413Z",
     "start_time": "2018-09-20T12:46:35.536368Z"
    }
   },
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/opt/anaconda3/lib/python3.5/site-packages/ipykernel_launcher.py:34: RuntimeWarning: divide by zero encountered in cdouble_scalars\n",
      "/opt/anaconda3/lib/python3.5/site-packages/ipykernel_launcher.py:34: RuntimeWarning: invalid value encountered in cdouble_scalars\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/opt/anaconda3/lib/python3.5/site-packages/ipykernel_launcher.py:34: RuntimeWarning: divide by zero encountered in cdouble_scalars\n",
      "/opt/anaconda3/lib/python3.5/site-packages/ipykernel_launcher.py:34: RuntimeWarning: invalid value encountered in cdouble_scalars\n"
     ]
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "%matplotlib inline\n",
    "import numpy as np\n",
    "import scipy.special as scpsp \n",
    "import matplotlib.pyplot as plt\n",
    "\n",
    "\n",
    "def theta(z):\n",
    "    ail = scpsp.airy(z)\n",
    "    ml = np.sqrt(ail[0]**2 + ail[2]**2)\n",
    "    thl = np.arctan2(ail[0],ail[2])\n",
    "    mllnp = (ail[0]*ail[1]+ail[2]*ail[3])/ml**2\n",
    "    thlp = 1./(np.pi*ml**2)\n",
    "    return thl \n",
    "\n",
    "def coeftransm(k=0.,a = 10.**(1./3.),alpha=1.):\n",
    "    zl = -(k * alpha)**2\n",
    "    zr = a/alpha + zl\n",
    "    ail = scpsp.airy(zl)\n",
    "    ml = np.sqrt(ail[0]**2 + ail[2]**2)\n",
    "    thl = np.arctan2(ail[0],ail[2])\n",
    "    mllnp = (ail[0]*ail[1]+ail[2]*ail[3])/ml**2\n",
    "    thlp = -1./(np.pi*ml**2)\n",
    "    \n",
    "    air = scpsp.airy(zr)    \n",
    "    mr = np.sqrt(air[0]**2 + air[2]**2)\n",
    "    thr = np.arctan2(air[0],air[2])\n",
    "    mrlnp = (air[0]*air[1]+air[2]*air[3])/mr**2\n",
    "    thrp = -1./(np.pi*mr**2)\n",
    "    \n",
    "    u = (1.j*k*alpha-mrlnp)*np.cos(thr)/thrp + np.sin(thr)\n",
    "    v = -(1.j*k*alpha-mrlnp)*np.sin(thr)/thrp + np.cos(thr)\n",
    "    al = (u*np.sin(thl)+v*np.cos(thl))*(1.j*k*alpha+mllnp)\n",
    "    al = al + thlp * ( u * np.cos(thl) - v * np.sin(thl) )\n",
    "    al = al/(2.*1.j*k*alpha)\n",
    "    t = mr**2/ml**2/(al*al.conj()).real\n",
    "    return (t,u,v)\n",
    "\n",
    "\n",
    "def coeftransm_app(k=0.,a = 10.**(1./3.),alpha=1.):\n",
    "    t=.5\n",
    "    k0 = np.sqrt(a/alpha**3)\n",
    "    if k > k0:\n",
    "        t=1- (.5*k0/k)**4 \n",
    "    elif k<k0:\n",
    "        if a/alpha>1:\n",
    "            t = 18.9\n",
    "            t = t * (k*alpha)**2*np.sqrt(a/alpha)\n",
    "            t = t * np.exp(-4./3.*(a/alpha)**1.5 * (1-(k/k0)**2)**1.5)\n",
    "        else:\n",
    "            t= 16.*(k/k0)**2/(a*k0)**2\n",
    "    if t>1:\n",
    "        t=np.nan\n",
    "    return (t,1-t)\n",
    "\n",
    "\n",
    "\n",
    "ks = np.linspace(0,4.,100)\n",
    "ens = ks**2\n",
    "\n",
    "a=1.\n",
    "k0=np.sqrt(a)\n",
    "ts = np.array([coeftransm(k,a=a)[0].real for k in ks])\n",
    "plt.plot(ks,ts,label=\"$a=\\\\alpha$\")\n",
    "tsapp = np.array([coeftransm_app(k,a=a)[0] for k in ks])\n",
    "plt.scatter(ks,tsapp,label=\"$a= \\\\alpha$ (approx)\",c=\"b\")\n",
    "\n",
    "plt.rc('text', usetex=True)\n",
    "plt.xlabel(\"k/k0\")\n",
    "plt.ylabel(\"T\")\n",
    "plt.title(\"Barrera intermedia\")\n",
    "plt.legend(loc=0)\n",
    "plt.savefig(\"figs/qI-1-05-transmision-1.png\")\n",
    "plt.show()\n",
    "\n",
    "####################################################################\n",
    "\n",
    "ks = np.linspace(0,4.,100)\n",
    "a=(10.**(1/3.))\n",
    "k0=np.sqrt(a)\n",
    "ts = np.array([coeftransm(k,a=a)[0].real for k in ks])\n",
    "plt.plot(ks,ts,label=\"$a=\\\\sqrt[3]{10} \\\\alpha$\")\n",
    "tsapp = np.array([coeftransm_app(k,a=a)[0] for k in ks])\n",
    "plt.scatter(ks,tsapp,label=\"$a=\\\\sqrt[3]{10} \\\\alpha$ (approx)\",c=\"b\")\n",
    "\n",
    "plt.rc('text', usetex=True)\n",
    "plt.xlabel(\"k/k0\")\n",
    "plt.ylabel(\"T\")\n",
    "plt.title(\"Barrera ancha\")\n",
    "plt.legend(loc=0)\n",
    "plt.savefig(\"figs/qI-1-05-transmision-2.png\")\n",
    "plt.show()\n",
    "\n",
    "\n",
    "\n",
    "ks = np.linspace(0,3.,100)\n",
    "a=(.1**(1/3.))\n",
    "k0=np.sqrt(a)\n",
    "ts = np.array([coeftransm(k,a=a)[0].real for k in ks])\n",
    "plt.plot(ks,ts,label=\"$a=\\\\sqrt[3]{.1} \\\\alpha$\")\n",
    "tsapp = np.array([coeftransm_app(k,a=a)[0] for k in ks])\n",
    "plt.scatter(ks,tsapp,label=\"$a=\\\\sqrt[3]{.1} \\\\alpha$ (approx)\",c=\"b\")\n",
    "\n",
    "plt.rc('text', usetex=True)\n",
    "plt.title(\"Barrera delgada\")\n",
    "plt.xlabel(\"k/k0\")\n",
    "plt.ylabel(\"T\")\n",
    "plt.legend(loc=4)\n",
    "plt.savefig(\"figs/qI-1-05-transmision-3.png\")\n",
    "plt.show()\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
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