QUANTUM EQUIVALENT OF THE BERTRAND'S THEOREM

Abstract

A procedure for constructing general bound state potentials is given. Analogous to the Bertrand's theorem in classical mechanics, we then identify radial eigenvalue problems possessing exact solvability and infinite number of eigenstates. Akin to the classical result, the only special cases of the general central potential, satisfying the above two conditions, are the Coulomb and harmonic oscillator potentials.