Quantum equivalent of the Bertrand's theorem
classification
🪐 quant-ph
keywords
potentialsbertrandboundcasescentralconditionsconstructingcoulomb
read the original 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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