Connection between closeness of classical orbits and the factorization of radial Schr\"odinger equation
Abstract
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\"odinger 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\"odinger equation. Some discussion was made about the factorization of a 1D Schr\"odinger equation.
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