Abstract
We discuss the equivalence of different forms of description of a quantum particle passing through a grating, in view of the approach based on the Schrödinger equation and the tomographic-probability approach. We show the equivalence of two forms of the solution to the Helmholtz equation for matter waves behind a diffraction grating, the first form being the Fresnel-Kirchhoff integral form and the second one, a superposition of transverse modes of the field. From this equivalence follows the equivalence of the corresponding two forms of the transverse wave function defined by assuming that the longitudinal motion is almost classical. This function has the important property that it is independent of the initial longitudinal momentum of the particle. The results are analyzed and interpreted using symplectic tomographic-probability distributions (tomograms).
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Arsenović, D., Božić, M., Man’ko, O.V. et al. Equivalence of two forms of the solution to the Schrödinger equation for a particle passing through a grating. J Russ Laser Res 26, 94–108 (2005). https://doi.org/10.1007/s10946-005-0009-1
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DOI: https://doi.org/10.1007/s10946-005-0009-1