Quantum equivalent of the Bertrand's theorem
Quantum Physics
2011-07-19 v1
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.
Keywords
Cite
@article{arxiv.quant-ph/9905011,
title = {Quantum equivalent of the Bertrand's theorem},
author = {N. Gurappa and Prasanta K. Panigrahi and T. Soloman Raju},
journal= {arXiv preprint arXiv:quant-ph/9905011},
year = {2011}
}
Comments
11 pages, REVTeX