How to express exp(kCos(gamma)) using spherical harmonics?

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The discussion centers on expressing the function exp(kCos(gamma)) using spherical harmonics. Participants recommend consulting advanced texts in mathematical physics, quantum mechanics, or electromagnetism for the expansion of plane waves in terms of spherical harmonics and Bessel functions. The application of these expansions is particularly relevant for use in transfer matrices.

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  • Understanding of spherical harmonics
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  • Knowledge of plane wave expansions
  • Basic concepts of transfer matrices in physics
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Mathematicians, physicists, and engineers interested in advanced mathematical techniques for wave functions and their applications in quantum mechanics and electromagnetism.

vanmil
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Hello all, i am looking for a relation to express exp(kCos(gamma)) in spherical harmonics. How can I express it?


thanks
 
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Look in any advanced text in math physics, quantum mechanics or E&M, what you are looking for is the expansion of a plane wave in terms of spherical harmonics and Bessel functions.
 
Thanks for your reply Dr. Transport, I want to use spherical harmonic expansions for exponential functions in a transfer matrix.
 

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