Bound state variational principle employing a discontinuous trial function

Abstract

A new variational principle for the bound state energy eigenvalues of a quantum system is presented. In it, not only ∇ψ(r) but also ψ(r) itself can be discontinuous across a surface. That is, the trial ψ(r) can have both a kink and a jump across a surface. This allows the use of different basis functions in different regions of space without having to impose any matching conditions across the surface. All parameters appearing in the principle can be variational parameters; none are needed to help invoke any continuity conditions on the trial function. Although the principle is not a definite (minimum) one, good results are obtained in several examples.