Extensions of the auxiliary field method to solve Schrödinger equations

Details Extensions of the auxiliary field method to solve Schrödinger equations Extensions of the auxiliary field method to solve Schrödinger equations

2008-06-12

arxiv.org/abs/0806.2020v1

J. Phys. A: Math. Theor. 41 (2008) 425301

Physics

Quantum Physics

Scientific paper

10.1088/1751-8113/41/42/425301

It has recently been shown that the auxiliary field method is an interesting tool to compute approximate analytical solutions of the Schr\"{o}dinger 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 $a P(r)+V(r)$, and several explicit examples are studied. Connections existing between the perturbation theory and the auxiliary field method are also discussed.

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