MOMENT-PROBLEM FORMULATION OF A MINIMAX QUANTIZATION PROCEDURE

The eigenvalue moment method (EMM) is a general theory for generating converging lower and upper bounds to the discrete, low-lying spectrum of Schrodinger 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, F(E)[u]=Min(sigma=0.1)[V(sigma,E)[u]\M(sigma,E)[u]\V(sigma,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)=Max(u)Min(sigma=0,1[V(sigma,E,S)[u]\S(sigma)-1M(sigma,E)[u]S(sigma)-1\V(sigma,E,S)], whose local maxima converge to the discrete energy states of the system. We discuss the relevant theory and present several examples.