Eur. Phys. J. Plus (2012) 127: 66
https://doi.org/10.1140/epjp/i2012-12066-2

Regular Article

Fourier optics and time evolution of de Broglie wave packets

Dipartimento di Fisica, Università di Genova, INFN, Sezione di Genova, Genova, Italy

^* e-mail: dillon@ge.infn.it

Received: 21 May 2012
Revised: 29 May 2012
Accepted: 30 May 2012
Published online: 20 June 2012

Abstract

It is shown that, under the conditions of validity of the Fresnel approximation, diffraction and interference for a monochromatic wave traveling in the z-direction may be described in terms of the spreading in time of the transverse (x, y wave packet. The time required for the evolved wave packet to yield identical patterns as given by standard optics corresponds to the time for the quantum to cross the optical apparatus. This point of view may provide interesting cues in wave mechanics and quantum physics education.