Low-lying states of two-dimensional double-well potentials

Abstract

Wavefunctions, energies and selected expectation values of the low-lying stationary states of two-dimensional double-well potentials are obtained from the long-time solutions of the corresponding time-dependent Schrödinger equation. The numerical method consists of transformation to a diffusion-like equation which is then solved by an alternating-direction, implicit, finite-difference method. The method is tested for cases in which the energies have been obtained by other methods. Then the dependence of the energies and other properties on the potential parameters is discussed on the basis of results for four states of 35 different sets of potential parameters including some that lead to pseudo-degeneracies.