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American Journal of Physics

Answer to Question ♯21 [‘‘Snell’s law in quantum mechanics,’’ Steve Blau and Brad Halfpap, Am. J. Phys. 63 (7), 583 (1995)]

Peter W. Milonni

Published Jul 1, 1996• 4 citations
Publisher

Abstract

The quantum mechanical description of reflection and refraction in terms of photons is further extrapolated. The probability amplitude for a photon to be found inside or outside the medium is derived.
DOI
10.1119/1.18465

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The concept of time refraction is introduced to describe the effects of a sudden change of the optical properties of a dielectric medium. This can be seen as the most elementary process associated with photon acceleration and frequency upshifting. The quantum theory of such a process shows that the initial wave splits into time-transmitted and time-reflected waves propagating in opposite directions after the occurrence of a time discontinuity of the refractive index. The time refraction laws, analogous to the well known Fresnel formulas and Snell's law, are also derived. It is shown that, in quantum terms, time refraction is equivalent to a squeezing transformation.