Iterative solutions to quantum-mechanical problems
Abstract
We have shown [Phys. Rev. Lett. 80, 3673 (1998)] that the wave-function representation Ψ(ξ)=∑jaj[E]ξjRβ(ξ), developed in either configuration or momentum space for a suitable reference function Rβ(ξ), defines a highly accurate, multidimensional, energy-quantization procedure, once the convergent zeros of the power-series expansion coefficients aj[E]=0 (j-->∞) are determined. In this paper we amplify the underlying analysis and also examine some of the consequences for generating accurate wave functions.
- Publication:
-
Physical Review A
- Pub Date:
- October 1998
- DOI:
- 10.1103/PhysRevA.58.2708
- Bibcode:
- 1998PhRvA..58.2708T
- Keywords:
-
- 03.65.Ge;
- 02.30.Hq;
- Solutions of wave equations: bound states;
- Ordinary differential equations