V. Fock studied the hydrogen atom problem in momentum space by projecting the space onto a 4-dimensional hyper-sphere. He found that as a consequence of the symmetry of the problem in this space the eigen-functions are the R4 spherical harmonics and that the eigenvalues are determined only by the principal quantum number n. In this chapter we note that if his method is applied to the 2-dimensional Kepler problem in momentum space, the eigenfunctions are the R3 spherical harmonics, Y1m, and the eigenvalues are determined only by the quantum number 1. These facts enable one to give a visualizable geometric discussion of the dynamical degeneracy.
| Identifer | oai:union.ndltd.org:pacific.edu/oai:scholarlycommons.pacific.edu:uop_etds-2601 |
| Date | 01 January 1965 |
| Creators | Shibuya, Tai-ichi |
| Publisher | Scholarly Commons |
| Source Sets | University of the Pacific |
| Detected Language | English |
| Type | text |
| Format | application/pdf |
| Source | University of the Pacific Theses and Dissertations |
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