Iterative solutions to quantum-mechanical problems

Abstract

We have shown [Phys. Rev. Lett. 80, 3673 (1998)] that the wave-function representation \ensuremath{\Psi}(\ensuremath{\xi})$={\ensuremath{\sum}}_{j}{a}_{j}[E]{\ensuremath{\xi}}^{j}{R}_{\ensuremath{\beta}}(\ensuremath{\xi}),$ developed in either configuration or momentum space for a suitable reference function ${R}_{\ensuremath{\beta}}(\ensuremath{\xi}),$ defines a highly accurate, multidimensional, energy-quantization procedure, once the convergent zeros of the power-series expansion coefficients ${a}_{j}[E]=0(\stackrel{\ensuremath{\rightarrow}}{j}\ensuremath{\infty})$ are determined. In this paper we amplify the underlying analysis and also examine some of the consequences for generating accurate wave functions.