Quantum equivalent of the Bertrand's theorem

Abstract

A procedure for constructing bound state potentials is given. We show that, under the natural conditions imposed on a radial eigenvalue problem, the only special cases of the general central potential, which are exactly solvable and have infinite number of energy eigenvalues, are the Coulomb and harmonic oscillator potentials.

11 pages, REVTeX

References in corpus (2)

• Connection between Calogero-Marchioro-Wolfes type few-body models and free oscillators
• Extension Of Bertrand's Theorem And Factorization Of The Radial Schrödinger Equation