A New Method to Derive Low-Lying N-Dimensional Quantum Wave Functions by Quadratures along a Single Trajectory
✍ Scribed by R Friedberg; T.D Lee; W.Q Zhao
- Publisher
- Elsevier Science
- Year
- 2001
- Tongue
- English
- Weight
- 214 KB
- Volume
- 288
- Category
- Article
- ISSN
- 0003-4916
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✦ Synopsis
We present a new method to derive low-lying N -dimensional quantum wave functions by quadrature along a single trajectory. The N -dimensional Schroedinger equation is cast into a series of readily integrable first-order ordinary differential equations. Our approach resembles the familiar W.K.B. approximation in one dimension, but is designed to explore the classically forbidden region and has a much wider applicability than W.K.B. The current method also provides a perturbation series expansion and the Green functions of the wave equation in the N -dimension, all by quadratures along a single trajectory. A number of examples are given for illustration, including a simple algorithm to evaluate the Stark effect in closed form to any finite order of the electric field.