The eigenvalue moment method (EMM) is a general theory for generating converging lower and upper bounds to the discrete, low-lying spectrum of Schrödinger Hamiltonians. Recently, Handy, Giraud, and Bessis [Phys. Rev. A 44, 1505 (1991)] developed a dynamical systems EMM formulation through the discovery of a fundamental convex function, ${\mathit{F}}_{\mathit{E}}$[u]=${\mathrm{Min}}_{\mathrm{\sigma }=0,1\mathrm{}}$〈${\mathit{V}}^{(\mathrm{\sigma },\mathit{E})}$ [u]‖${\mathit{M}}^{(\mathrm{\sigma },\mathit{E})}$[u]‖${\mathit{V}}^{(\mathrm{\sigma },\mathit{E})}$[u]〉. By incorporating this within the c-shift EMM theory of Handy and Lee [J. Phys. A 24, 1565 (1991)], there results an alternative quantization procedure involving the function V(E)=${\mathrm{Max}}_{\mathit{u}}$${\mathrm{Min}}_{\mathrm{\sigma }=0,1\mathrm{}}$〈${\mathit{V}}^{\mathrm{\sigma },\mathit{E},\mathit{S})}$[u] ‖${\mathit{S}}_{\mathrm{\sigma }}^{\mathrm{-}1}$${\mathit{M}}^{(\mathrm{\sigma },\mathit{E})}$[u]${\mathit{S}}_{\mathrm{\sigma }}^{\mathrm{-}1}$‖ ${\mathit{V}}^{(\mathrm{\sigma },\mathit{E},\mathit{S})}$〉, whose local maxima converge to the discrete energy states of the system. We discuss the relevant theory and present several examples.

• Received 18 August 1993

DOI:https://doi.org/10.1103/PhysRevA.50.988