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Connection between closeness of classical orbits and the factorization of radial Schr\"{o}dinger equation
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.Comment: 14 pages, no figure
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