Variational solutions of simple quantum systems subject to variable boundary conditions. I. A model for physisorption

摘要

A variational solution to a model problem of a hydrogen atom near a sharp planar surface of a semihyphen;infinite substrate is studied. Results are presented for the ground and excited eigenstates and dipole moments of the hydrogen atom as a function of distance from the surface for two models: (a) a system in which the halfhyphen;space occupied by the solid is represented by an infinite potential step; and (b) a system in which the semihyphen;infinite substrate is perfectly imaging subject to a boundary condition that excludes the atomic electron from the substrate. Model (b) is considered as an idealized model for physisorption, where the exclusion of the electron simulates the exchange repulsion originating from the overlap of the atomic and substrate electrons. Results for the physisorption holding potential as a function of distance from the plane are presented and discussed.