Variational representation of the Dirac-Coulomb Hamiltonian with no spurious roots
- 1 June 1985
- journal article
- research article
- Published by American Physical Society (APS) in Physical Review A
- Vol. 31 (6) , 3541-3549
- https://doi.org/10.1103/physreva.31.3541
Abstract
A new approach to the variational representation of the Dirac equation is presented. The method takes advantage of the conditions satisfied by the eigenfunctions at the origin. In this way, a variational representation of the complete Dirac-Coulomb spectrum without spurious roots is obtained. Rigorous proofs of bounds for the positive and negative variational eigenvalues, as well as differential and integral properties of the variational eigenfunctions, are given. An alternative approach to the elimination of spurious roots based on constraining the basis set to satisfy the right nonrelativistic limit is also presented.Keywords
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