Bounds to the energy of quantum-mechanical models from variational functionals

Abstract

We derive semiclassical energy functions in configuration space that provide upper or lower bounds to the energies of quantum-mechanical systems. The bounds are predicted by rigorous theorems about the local energy which we choose to depend on adjustable parameters in order to improve the accuracy of the results. We apply the method to one-dimensional models, central-field systems, and the Zeeman effect in hydrogen.

Transition states and the critical parameters of central potentials

“…Since then many authors have contributed to the study of this problem. Among them we would like to refer to the works [3][4][5][6][7] and to emphasize particularly the contribution of Calogero and Brau [8][9][10][11][12].…”