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arXiv · 0903.3181

Semirelativistic Hamiltonians and the auxiliary field method

Bernard Silvestre-Brac·Claude Semay·Fabien Buisseret
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Abstract

Approximate analytical closed energy formulas for semirelativistic Hamiltonians of the form $σ\sqrt{\bm p^{2}+m^2}+V(r)$ are obtained within the framework of the auxiliary field method. This method, which is equivalent to the envelope theory, has been recently proposed as a powerful tool to get approximate analytical solutions of the Schrödinger equation. Various shapes for the potential $V(r)$ are investigated: power-law, funnel, square root, and Yukawa. A comparison with the exact results is discussed in detail.

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Bernard Silvestre-Brac, Claude Semay, Fabien Buisseret. 2009-03-18. Semirelativistic Hamiltonians and the auxiliary field method. https://doi.org/10.1142/s0217751x09045960

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