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* Add files via upload * Added project blanks * use os.path.join for audio files * Added projects * Updated docs/index.md * Add files via upload * Add files via upload * Add files via upload * Add files via upload * Add files via upload * Add files via upload * Add files via upload * Add files via upload * Add files via upload * Updates * Fix up README.md * commited clear version of nb * commited clear version of nb * Added explanations to projects * Add files via upload * Update notebooks * temp add version 2 of higgs * updated higgs search * Higgs project * Update docs/Projects.md * Updated nb * updated for final week Co-authored-by: bsafvato <[email protected]>
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# Mass Nevts | ||
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# Follow up notes for week 8. | ||
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### Frequency and wave number | ||
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Last week we worked with analyzing data using Fourier analysis. | ||
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In the first notebook we worked with audio files and looked at the frequencies that were | ||
present is a few music clips. | ||
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In the second notebook we worked with some data from Ben's lab studying the behavior of | ||
electrons on a copper surface. Basically, this introduced two new concepts. | ||
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1. We can apply Fourier analysis to spatial data as well as time data. I.e., with music, the frequency of the | ||
variation of the sound wave with time is what our ears hear as the pitch of the music. It turns out that the | ||
spatial frequency of variation of the electron density with distance is released to the momentum and energy | ||
levels of the electrons. | ||
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2. We can apply Fourier analysis in more that one dimension. I.e., we can study wave on surfaces, or even waves | ||
in solid materials. | ||
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Let's see if we can break those two concept down into pieces. | ||
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One of the figures we had showed waves that were oriented diagonally. | ||
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[Waves](!diagonal_waves.png) | ||
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The bright bits might be places where the wave is higher, the dark bits where it is lower. | ||
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The first concept we have is wave number. it is basically the spatial equivalent of frequency. I.e., it is the number | ||
of waves that you can fit into a fixed length. Since the image above is 1m X 1m it is really easy to count how many | ||
wave can fit in a meter. I count 10 waves along the x-axis and 5 waves along the y-axis. | ||
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The second concept is describing the wave in more that one dimension. But we have already basically done that. | ||
I.e., the wave numbers are 5 and 10, so we can combine them to get a wave vector, which is (5, 10). | ||
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We had a figure that looked like this: | ||
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[Waves](!diagonal_wave_vector.png) | ||
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The reason that there are two points instead of just 1 is that we just as easily count have counted in other other directions, | ||
e.g., left-to-right instead of right-to-left. | ||
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