Auxiliary field method and analytical solutions of the Schrödinger equation with exponential potentials

Details Auxiliary field method and analytical solutions of the Schrödinger equation with exponential potentials Auxiliary field method and analytical solutions of the Schrödinger equation with exponential potentials

2008-11-03

arxiv.org/abs/0811.0287v1

J. Phys. A: Math. Theor. 42 (2009) 245301

Physics

Quantum Physics

Scientific paper

10.1088/1751-8113/42/24/245301

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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