Solution of the Dirac Equation using the Lanczos Algorithm

2007/06/15 by R. C. Andrew, H. G. Miller, Andrew, R. C. +3
Computer Science · Mathematics · Physics and Astronomy · #Algebraic and Geometric Analysis #Matrix Theory and Algorithms #math-ph #math.GM #math.MP

paper · pdf · doi:10.48550/arxiv.0706.2236

arxiv created 2007/06/15 · arxiv updated 2009/12/01

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.

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