It is suggested that the supersymmetric WKB (SWKB) method may be useful in studying the deviation of the energy levels of a quantum system due to the presence of a spherically confining boundary. For illustration, we present the explicit results for the Coulomb and three-dimensional harmonic-oscillator potentials. It is observed that the confining geometry removes the angular-momentum degeneracy of the electronic energy levels of a free atom. Our predicted energy eigenvalues are in agreement with the exact ones obtained numerically.

• Received 24 March 1995

DOI:https://doi.org/10.1103/PhysRevA.52.1750