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 PSI must vanish on the bounding surface of the region, the trial function psi 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 -integral psi del2 psidtau and integral (del psi) . (del psi)dtau in the ratio 2: - 1. Although the principle is not a definite (minimum) one, good results are obtained in several examples.