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arXiv · 1709.07061

A Review of the Min-Max Approach to the Solution of Relativistic Electron Wave Equation

Sambhu Nath Datta
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Abstract

The variation problem associated with the solution of Dirac's relativistic electron equation is reviewed here. Derivation of the min-max theorem is discussed. A new observation is that the spurious roots of negative energy satisfy a max-min theorem. The min-max principle (MMP) for solution of Dirac equation, extendable to the Dirac-Fock case, is concisely reviewed. MMP for two-electron Dirac-Coulomb equation is discussed. The min-max theorem is physically interpreted for both Dirac and Dirac-Coulomb problems. Applications of MMP are collated in tables. Associated theoretical and computational developments are outlined. Limitations of MMP are spelt out and recent mathematical developments are discussed.

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Sambhu Nath Datta. 2017-09-19. A Review of the Min-Max Approach to the Solution of Relativistic Electron Wave Equation. https://arxiv.org/abs/1709.07061

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