Quantum equivalent of the Bertrand's theorem

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