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Physical Review

A Note on Weinstein's Variational Method

Walter Kohn

Published Jun 15, 1947• 28 citations
Publisher

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 $(n+1)\ensuremath{-}\mathrm{s}\mathrm{t}$ level is known; and (2) an upper bound for the $n$-th level if an upper bound for the $(n\ensuremath{-}1)\ensuremath{-}\mathrm{s}\mathrm{t}$ level is known.

DOI
10.1103/physrev.71.902

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