Phase-integral approach to quantal two- and three-dimensional isotropic anharmonic oscillators

Abstract

A two- or three-dimensional quantal isotropic anharmonic oscillator is treated by means of the phase-integral method of Fr\"oman and Fr\"oman. The generalized Bohr-Sommerfeld quantization condition for the radial wave function is expressed in terms of complete elliptic integrals up to the fifth order of the phase-integral approximation. The quantization condition is solved numerically, and energy levels are obtained for various quantum numbers. Comprison with numerically exact results is also made.