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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 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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http://hal.in2p3.fr/in2p3-00289591
Contributor : Emmanuelle Vernay <>
Submitted on : Monday, June 23, 2008 - 11:19:39 AM
Last modification on : Thursday, November 19, 2020 - 12:58:50 PM

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B. Silvestre-Brac, C. Semay, F. Buisseret. Extensions of the auxiliary field method to solve Schrödinger equations. Journal of Physics A: Mathematical and Theoretical, IOP Publishing, 2008, 41, pp.425301. ⟨10.1088/1751-8113/41/42/425301⟩. ⟨in2p3-00289591⟩

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