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Perturbation theory for the Stark effect in a double δ quantum well

Gabriel Álvarez1 and Bala Sundaram2

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We study the Stark effect in a symmetric double δ quantum well, for which there are two kinds of resonances: the familiar resonances stemming from the bound states, and a doubly infinite family of resonances stemming from the zero-field continuum threshold. We derive explicit expressions for the Borel-summable Rayleigh–Schrödinger perturbation series for the resonances stemming from the bound states, for the imaginary part of these same resonances and for all the resonances stemming from the zero-field continuum threshold. The techniques used in this paper are directly applicable to realistic models of quantum square well potentials with or without barriers.


PACS

32.60.+i Zeeman and Stark effects

02.30.Lt Sequences, series, and summability

31.15.xp Perturbation theory

MSC

34E10 Perturbations, asymptotics

Subjects

Atomic and molecular physics

Mathematical physics

Computational physics

Dates

Issue 41 (15 October 2004)

Received 2 June 2004, in final form 1 September 2004

Published 29 September 2004



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