EXTENSION OF A MOMENT-PROBLEM MINIMAX QUANTIZATION PROCEDURE TO ANHARMONIC POTENTIALS

Recently, Handy, Appiah, and Bessis (HAB) [Phys. Rev. A 50, 988 (1994)] showed that the local maxima in the energy variable E of the function V(E)=max(u)min(sigma)lambda(E)(sigma)[(u) over right arrow] (where lambda(E)(sigma)[(u) over right arrow] are the smallest eigenvalues of modified Hankel moment matrices) approximate the discrete energy states of Schrodinger Hamiltonians. Their theoretical result was demonstrated by way of two zero-missing-moment problems, the harmonic oscillator and the x(2) + lambda[x(2)/(1 + gx(2))] potentials, for which the corresponding eigenvalue functions lambda(E)(sigma) are solely energy dependent. We examine the general n-missing-moment problem through an application of gradient optimization techniques that are suitable for piecewise differentiable functions, thereby enabling us to test HAB's results for anharmonic potentials of-missing-moment order 1, 2, and 3, corresponding to the quartic, sextic, and octic anharmonic potentials, respectively.