R W Robinett 2010 Eur. J. Phys. 31 1 doi:10.1088/0143-0807/31/1/001
R W Robinett
Show affiliationsWe 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.
Issue 1 (January 2010)
Received 24 June 2009, in final form 2 September 2009
Published 4 November 2009
R W Robinett 2010 Eur. J. Phys. 31 1
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