Connection between closeness of classical orbits and the factorization of radial Schrödinger equation

Details Connection between closeness of classical orbits and the factorization of radial Schrödinger equation Connection between closeness of classical orbits and the factorization of radial Schrödinger equation

1999-11-03

arxiv.org/abs/hep-ph/9911217v2

Phys.Rev.A58:862,1998

Physics

High Energy Physics

High Energy Physics - Phenomenology

14 pages, no figures

Scientific paper

10.1103/PhysRevA.58.862

It was shown that the Runge-Lenz vector for a hydrogen atom is equivalent to the raising and lowering operators derived from the factorization of radial Schr\"{o}dinger equation. Similar situation exists for an isotropic harmonic oscillator. It seems that there may exist intimate relation between the closeness of classical orbits and the factorization of radial Schr\"{o}dinger equation. Some discussion was made about the factorization of a 1D Schr\"{o}dinger equation.

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