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Solution of the Dirac Equation using the Lanczos Algorithm

Mathematical Physics 2007-06-18 v1 General Mathematics math.MP

Abstract

Covergent eigensolutions of the Dirac Equation for a relativistic electron in an external Coulomb potential are obtained using the Lanczos Algorithm. A tri-diagonal matrix representation of the Dirac Hamiltonian operator is constructed iteratively and diagonalized after each iteration step to form a sequence of convergent eigenvalue solutions. Any spurious solutions which arise from the presence of continuum states can easily be identified.

Keywords

Cite

@article{arxiv.0706.2236,
  title  = {Solution of the Dirac Equation using the Lanczos Algorithm},
  author = {R. C. Andrew and H. G. Miller and G. D. Yen},
  journal= {arXiv preprint arXiv:0706.2236},
  year   = {2007}
}
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