Quantum equivalent of the Bertrand's theorem

Details Quantum equivalent of the Bertrand's theorem Quantum equivalent of the Bertrand's theorem

1999-05-05

arxiv.org/abs/quant-ph/9905011v1

Mod.Phys.Lett.A15:1851-1858,2000

Physics

Quantum Physics

11 pages, REVTeX

Scientific paper

10.1142/S0217732300002255

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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