Extensions of the auxiliary field method to solve Schrödinger equations

Abstract

It has recently been shown that the auxiliary field method is an interesting tool to compute approximate analytical solutions of the Schrödinger equation. This technique can generate the spectrum associated with an arbitrary potential $V(r)$ starting from the analytically known spectrum of a particular potential $P(r)$. In the present work, general important properties of the auxiliary field method are proved, such as scaling laws and independence of the results on the choice of $P(r)$. The method is extended in order to find accurate analytical energy formulae for radial potentials of the form $aP(r)+V(r)$, and several explicit examples are studied. Connections existing between the perturbation theory and the auxiliary field method are also discussed.

References in corpus (4)

• On two- and three-body descriptions of hybrid mesons
• Auxiliary fields and hadron dynamics
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• Auxiliary fields as a tool for computing analytical solutions of the Schrödinger equation

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• Mass Formula for Light Nonstrange Mesons and Regge Trajectories in Quark Model
• Further developments for the auxiliary field method