Exponential Solution of the Schrödinger Equation: Potential Scattering
- 15 March 1969
- journal article
- research article
- Published by AIP Publishing in The Journal of Chemical Physics
- Vol. 50 (6), 2517-2525
- https://doi.org/10.1063/1.1671410
Abstract
The exponential matrix method of Magnus is applied to the solution of the time‐independent Schrödinger equation for potential scattering. The formal properties of this method as a numerical technique are analyzed and the close connections to the WKBJ approximation are also shown. The use of the Magnus series is shown to yield the correct behavior near the origin without the Langer modification of the WKBJ equation. Applications to the scattering from above a potential barrier and to the phase shifts for a Lennard‐Jones (12–6) potential are given.Keywords
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