A Padé Extrapolated Inverse Power Method for Coupled Schrödinger-like Equations Applied to the Two-Body Relativistic Bound State Problem in Quantum Electrodynamics
✍ Scribed by H.W. Crater
- Publisher
- Elsevier Science
- Year
- 1994
- Tongue
- English
- Weight
- 651 KB
- Volume
- 115
- Category
- Article
- ISSN
- 0021-9991
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✦ Synopsis
We adapt the inverse power method to the solution of the eigenvalue problem associated with recently developed forms of coupled two-body Dirac equations. A Pauli reduction of these equations leads to coupled Schrödinger-like equations which we solve using central difference methods. Our adaptation therefore requires an efficient inversion of large blocked and banded matrices and for the case of interactions derived from lowest order quantum electrodynamics we show how this method can be used, in conjunction with logarithmic scaling and Padé extrapolation techniques. to obtain numerical solutions for the positronium and muonium spectrum that agree with perturbation theory through order (m \alpha^{4}) (with error on the order of (m x^{6}) ). 1994 Academic Press, Inc.