Abstract
Variational perturbation theory was used to solve the Schrödinger equation for a hydrogen atom confined at the center of an impenetrable cavity. Ground state and excited state energies and expectation values calculated from the perturbation wavefunction are comparable in accuracy to results from direct numerical solution.
Highlights
Confined quantum mechanical systems are a useful model for simulating the effect of external conditions on an enclosed atom
Application of Rayleigh-Schrödinger perturbation theory to confined systems is complicated by the lack of closed form zero-order wavefunctions
When a zero-order wavefunction can be obtained, variational perturbation theory provides a method to carry the calculation to high order
Summary
Confined quantum mechanical systems are a useful model for simulating the effect of external conditions on an enclosed atom. Application of Rayleigh-Schrödinger perturbation theory to confined systems is complicated by the lack of closed form zero-order wavefunctions. When a zero-order wavefunction can be obtained, variational perturbation theory provides a method to carry the calculation to high order.
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