Auxiliary field method and 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 Schrödinger 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 Schrödinger 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.

References in corpus (9)

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Cited by in corpus (9)

• The quantum N-body problem and the auxiliary field method
• Numerical tests of the envelope theory for few-boson systems
• Semirelativistic Hamiltonians and the auxiliary field method
• The auxiliary field method in quantum mechanics
• Duality relations in the auxiliary field method
• Eigenstates with the auxiliary field method
• Further developments for the auxiliary field method
• About disposition of energy levels
• Upper bounds for critical coupling constants for binding some quantum many-body systems