Semi-Classical Study of a Hydrogenic Atom near a Rigid Wall

A semi-classical calculation of the discrete electronic spectrum for a hydrogenic atom located near a rigid wall, and the corresponding graphics of some of the energy levels as function of the nucleus–wall distance are presented. Calculations are based on the exact analytic solution of Newton equations of motion within a model which considers elastic collisions (EC) at the wall, followed by a primitive WKB quantization. This system can be used as a model for 2D and 3D quantum devices, such as shallow state of an impurity atom or Wannier-Mott exciton near to interfaces.