A Laguerre Polynomial Orthogonality and the Hydrogen Atom

Details A Laguerre Polynomial Orthogonality and the Hydrogen Atom A Laguerre Polynomial Orthogonality and the Hydrogen Atom

2000-11-13

arxiv.org/abs/math-ph/0011021v2

Analysis & Appl. 1 (2003), 177-188

Physics

Mathematical Physics

13 pages, LaTeX, new section on Meixner polynomials

Scientific paper

The radial part of the wave function of an electron in a Coulomb potential is the product of a Laguerre polynomial and an exponential with the variable scaled by a factor depending on the degree. This note presents an elementary proof of the orthogonality of wave functions with differing energy levels. It is also shown that this is the only other natural orthogonality for Laguerre polynomials. By expanding in terms of the usual Laguerre polynomial basis an analogous strange orthogonality is obtained for Meixner polynomials.

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