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arXiv · quant-ph/9905011

Quantum equivalent of the Bertrand's theorem

N. Gurappa·Prasanta K. Panigrahi·T. Soloman Raju
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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.

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N. Gurappa, Prasanta K. Panigrahi, T. Soloman Raju. 1999-05-05. Quantum equivalent of the Bertrand's theorem. https://doi.org/10.1142/s0217732300002255

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