In a quantum mechanical description of the Kapitza-Dirac effect the vector potential (2.1) enters
into the corresponding wave equation of the electron motion. The solution of this equation is, in general,
demanding because of the separate space and time dependencies of the standing wave potential.
For non-relativistic electron dynamics based on the Schrödinger equation, it has been shown that the
effect of the vector potential can be well approximated by a static scalar potential [40, 41].
http://pubman.mpdl.mpg.de/pubman/item/escidoc:1567351:3/component/escidoc:1567350/2012_dissertation_Ahrens.pdf
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