Equivalent power law potentials

Abstract

It is shown that the radial Schroedinger equation for a power law potential and a particular angular momentum may be transformed using a change of variable into another Schroedinger equation for a different power law potential and a different angular momentum. It is shown that this leads to a mapping of the spectra of the two related power law potentials. It is shown that a similar correspondence between the classical orbits in the two related power law potentials exists. The well known correspondence of the Coulomb and oscillator spectra is a special case of a more general correspondence between power law potentials.

arXiv comment10 pages. Typographical mistakes in the earlier version are corrected

Cited by in corpus (2)

• Power-Duality in Path Integral Formulation of Quantum Mechanics
• Two quantum particles trapped in three dimensions harmonic oscillator and interacting via finite range soft-core interaction