Damped relaxation techniques to calculate relativistic bound states
- 1 October 1989
- journal article
- research article
- Published by American Physical Society (APS) in Physical Review A
- Vol. 40 (8), 4182-4189
- https://doi.org/10.1103/physreva.40.4182
Abstract
We discuss a class of damped relaxation methods for finding stationary (bound-state) solutions of relativistic wave equations represented by matrix equations on a discrete space lattice. Model calculations are presented for the Schrödinger and Dirac equations using a point-Coulomb potential for which analytic solutions can be obtained. A numerical application using a Gaussian potential in one dimension illustrates the general procedure for practical applications. As a realistic example, we study the Dirac equation on a three-dimensional Cartesian lattice using the Coulomb potential of a uniform charge distribution.Keywords
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