Exact L2 series solution of the Dirac-Coulomb problem for all energies

Details Exact L2 series solution of the Dirac-Coulomb problem for all energies Exact L2 series solution of the Dirac-Coulomb problem for all energies

2004-05-03

arxiv.org/abs/hep-th/0405023v1

Ann.Phys.312:144-160,2004

Physics

High Energy Physics

High Energy Physics - Theory

14 pages

Scientific paper

10.1016/j.aop.2004.01.011

We obtain exact solution of the Dirac equation with the Coulomb potential as an infinite series of square integrable functions. This solution is for all energies, the discrete as well as the continuous. The spinor basis elements are written in terms of the confluent hypergeometric functions and chosen such that the matrix representation of the Dirac-Coulomb operator is tridiagonal. The wave equation results in a three-term recursion relation for the expansion coefficients of the wavefunction which is solved in terms of the Meixner-Pollaczek polynomials.

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