Perturbation theory for the hydrogen atom in a spherical cavity with off-centre nucleus

Abstract

The problem of a hydrogen atom in an impenetrable spherical cavity of small radius Ris considered on the basis of the first-order perturbational treatment of the electron-nucleus interaction taking explicit account of the boundary condition. An approximate analytic expression is derived for the electronic energy as a function of the shift of the nucleus off the centre. The estimations obtained are in good qualitative and semiquantitative agreement with the results of the finite-difference calculations. Some general features of the energy dependences are discussed qualitatively.