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Auxiliary fields as a tool for computing analytical solutions of the Schrödinger equation

Abstract : We propose a new method to obtain approximate solutions for the Schr\"{o}dinger equation with an arbitrary potential that possesses bound states. This method, relying on the auxiliary field technique, allows in many cases to find analytical solutions. It offers a convenient way to study the qualitative features of the energy spectrum of bound states in any potential. In particular, we illustrate our method by solving the case of central potentials with power-law form and with logarithmic form. For these types of potentials, we propose very accurate analytical energy formulae which improve a lot the corresponding formulae that can be found in literature.
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http://hal.in2p3.fr/in2p3-00258964
Contributor : Emmanuelle Vernay <>
Submitted on : Tuesday, February 26, 2008 - 11:10:56 AM
Last modification on : Monday, July 20, 2020 - 9:18:24 AM

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B. Silvestre-Brac, C. Semay, F. Buisseret. Auxiliary fields as a tool for computing analytical solutions of the Schrödinger equation. Journal of Physics A: Mathematical and Theoretical, IOP Publishing, 2008, 41, pp.275301. ⟨10.1088/1751-8113/41/27/275301⟩. ⟨in2p3-00258964⟩

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