Variational principle for confined quantum systems

A new variational principle for the energy eigenvalues of a confined quantum system is presented. Whereas the exact wave function Ψ must vanish on the bounding surface of the region, the trial function ψ in this principle need not obey any specific boundary condition. Calculationally, the method is similar to the conventional variational method except that kinetic energy turns out to be a weighted average of -Fψ${\mathrm{\nabla }}^2$ψ dτ and F(∇ψ)⋅(∇ψ)dτ in the ratio 2:-1. Although the principle is not a definite (minimum) one, good results are obtained in several examples.