On the Temple lower bound for eigenvalues

Abstract

The author examines the relation between the Temple, Weinstein and Stevenson bounds for an arbitrary eigenvalues of a Hamiltonian H. It is shown that, in a sense which is defined, the Temple and Stevenson bounds are numerically equivalent, while the Weinstein bound is inferior to either. The Temple bound is reformulated and it is shown that the usual restriction on its validity may be relaxed; the relaxation leads to rather more convenient calculations in the presence of excited states, but not to improved lower bounds. A numerical example demonstrating the extension is given.