The energy levels and the corresponding normalized wave functions for a model of a compressed atom. II

Abstract

Recently Fröman et al. [J. Math. Phys. 28, 1813 (1987)] obtained a simple formula for the energy shift due to the compression of an atom. In the model considered the usual condition (associated with the corresponding uncompressed atom) that the wave function must vanish at r=∞ is replaced by the boundary condition that the wave function must have a node at the finite distance r=a. The treatment of the problem of obtaining the energy shift due to the compression is based on the phase-integral method developed by Fröman and Fröman. In the present work the formula for the energy shift is generalized to a possible additional choice of the base function in the phase-integral treatment. The normalized wave function close to the origin is also obtained. As an application, the resulting general formula for the energy shift is particularized to the case of a hydrogenic atom and a numerical illustration of the accuracy of the formula for the two alternative choices of the base function is given.