The problem of a hydrogen atom in a cavity: Oscillator representation solution versus analytic solution

Abstract A solution to the problem of a hydrogenic atom in homogeneous dielectric medium with concentric spherical cavity using oscillator representation method (ORM) is presented. The results obtained by ORM are compared known exact analytic solution. energy levels exhibit shallow-deep instability as function radius. sharpness transition depends on value constant medium. agree well when not too sharp (i.e., large) for all values zeroth order approximation diverge significantly region radius where occurs) high and result sharp. Even transition, again very at least ground state commonly used removed. methodology model presented this article can potentially be two-electron systems quantum dot.