Semirelativistic Hamiltonians and the auxiliary field method

Details Semirelativistic Hamiltonians and the auxiliary field method Semirelativistic Hamiltonians and the auxiliary field method

2009-03-18

arxiv.org/abs/0903.3181v1

Int. J. Mod. Phys. A 24, 4695 (2009)

Physics

Quantum Physics

Scientific paper

10.1142/S0217751X09045960

Approximate analytical closed energy formulas for semirelativistic Hamiltonians of the form $\sigma\sqrt{\bm p^{2}+m^2}+V(r)$ 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 Schr\"odinger 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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