# The auxiliary field method and approximate analytical solutions of the Schrödinger equation with exponential potentials

Abstract : The auxiliary field method is a new and efficient way to compute approximate analytical eigenenergies and eigenvectors of the Schr\"{o}dinger equation. This method has already been successfully applied to the case of central potentials of power-law and logarithmic forms. In the present work, we show that the Schr\"{o}dinger equation with exponential potentials of the form $-\alpha r^\lambda \exp(-\beta r)$ can also be analytically solved by using the auxiliary field method. Formulae giving the critical heights and the energy levels of these potentials are presented. Special attention is drawn on the Yukawa potential and the pure exponential one.
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Journal articles
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Submitted on : Tuesday, November 4, 2008 - 8:27:44 AM
Last modification on : Thursday, November 19, 2020 - 12:58:42 PM

### Citation

B. Silvestre-Brac, C. Semay, F. Buisseret. The auxiliary field method and approximate analytical solutions of the Schrödinger equation with exponential potentials. Journal of Physics A: Mathematical and Theoretical, IOP Publishing, 2008, 42, pp.245301. ⟨10.1088/1751-8113/42/24/245301⟩. ⟨in2p3-00336420⟩

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