# Semirelativistic hamiltonians and the auxiliary field method

Abstract : 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 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.
Document type :
Journal articles

http://hal.in2p3.fr/in2p3-00369281
Contributor : Emmanuelle Vernay <>
Submitted on : Thursday, March 19, 2009 - 8:10:45 AM
Last modification on : Thursday, November 19, 2020 - 12:58:51 PM

### Citation

B. Silvestre-Brac, C. Semay, F. Buisseret. Semirelativistic hamiltonians and the auxiliary field method. International Journal of Modern Physics A, World Scientific Publishing, 2009, 24, pp.4695-4726. ⟨10.1142/S0217751X09045960⟩. ⟨in2p3-00369281⟩

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