2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/131811Covergent 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.Mathematical PhysicsGeneral Mathematicstext