A Note on Weinstein's Variational Method

Abstract

Weinstein's modification of the Ritz principle is used to derive (1) a lower bound for the $n$-th energy-level of a quantum mechanical system if a lower bound for the $\mathrm{}(n+1\mathrm{})\mathrm{}-\mathrm{s}\mathrm{t}$ level is known; and (2) an upper bound for the $n$-th level if an upper bound for the $\mathrm{}(n-1\mathrm{})\mathrm{}-\mathrm{s}\mathrm{t}$ level is known.