Solution for bound state wavefunctions and matrix elements by the piecewise analytic method

Abstract

The solution of multidimensional bound state problems in quantum mechanics by the piecewise analytic method introduced by Gordon is discussed in detail. The numerical techniques necessary to calculate the wavefunctions and matrix elements are presented. An efficient least squares method for fitting the potential energy function to spectroscopic frequencies is described. Tests of the accuracy of the piecewise analytic method have been performed and the results are given. The techniques presented here are especially advantageous for systems in which the motion along the several coordinates is strongly coupled (beyond the perturbation theory limit).