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Open Quantum Systems Decoherence Quantum Simulation

Relativistic Coulomb Integrals and Zeilberger's Holonomic Systems Approach. I

arXiv
Authors: Peter Paule, Sergei K. Suslov

Year

2012

Paper ID

8683

Status

Preprint

Abstract Read

~2 min

Abstract Words

83

Citations

N/A

Abstract

With the help of computer algebra we study the diagonal matrix elements <Or^p>, where O are the standard Dirac matrix operators and the angular brackets denote the quantum-mechanical average for the relativistic Coulomb problem. Using Zeilberger's extension of Gosper's algorithm and a variant to it, three-term recurrence relations for each of these expectation values are derived together with some transformation formulas for the corresponding generalized hypergeometric series. In addition, the virial recurrence relations for these integrals are also found and proved algorithmically.

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  • With the help of computer algebra we study the diagonal matrix elements , where O are the standard Dirac matrix operators and the angular brackets denote the quantum-mechanical...

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References & Citation Signals

[1] DOI https://doi.org/arXiv:1206.2071 [2] arXiv https://arxiv.org/abs/1206.2071 [3] Publisher https://arxiv.org/abs/1206.2071

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