The Stark effect in linear potentials

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Abstract

We examine the Stark effect (the second-order shifts in the energy spectrum due to an external constant force) for two one-dimensional model quantum mechanical systems described by linear potentials, the so-called quantum bouncer (defined by V(z) = Fz for z > 0 and V(z) = ∞ for z < 0) and the symmetric linear potential (given by V(z) = F|z|). We show how straightforward use of the most obvious properties of the Airy function solutions and simple Taylor expansions gives closed form results for the Stark shifts in both systems. These exact results are then compared to other approximation techniques, such as perturbation theory and WKB methods. These expressions add to the small number of closed-form descriptions available for the Stark effect in model quantum mechanical systems.

Original languageEnglish (US)
Pages (from-to)1-13
Number of pages13
JournalEuropean Journal of Physics
Volume31
Issue number1
DOIs
StatePublished - 2010

All Science Journal Classification (ASJC) codes

  • Physics and Astronomy(all)

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