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}
}