Take a 600-cell in 4D with 120 vertices ±v_i, i=1…60 Define F(x)=𝚷_i v_i·x Stereographically project F from a 4-sphere to 3D, then Fourier-transform from momentum space to position space. Result: this hydrogen wave function, with energy level n=61. https://www.gregegan.net/SCIENCE/SymmetricWaves/SymmetricWaves.html …pic.twitter.com/DdYMD55XsY
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Replying to @gregeganSF @IanAdAstra
If anyone could point me to a progression of books, online classes or other resources to get me up to a level where I could attempt to understand this I would appreciate it. I know the basic concept of projecting from higher to lower spatial dimensions, but not the math.
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Replying to @kesmeby @IanAdAstra
Stereographic projection isn’t complicated. Wikipedia gives the formulas for 3D to 2D, which generalise in the obvious way. https://en.wikipedia.org/wiki/Stereographic_projection#First_formulation … The other material requires polynomials, partial differential equations, and Fourier transforms at 1st year undergrad level.
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Alas, relatively few 1st year undergrads study the Fourier transform these days (much less partial differential equations.)
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