Diffraction in time of matter waves located in a confined region

Abstract

The process of diffraction in time of a standing matter wave is studied. This case occurs generally when a quantum particle is confined in a trap or infinite potential well. First of all, the wave-function of a classical time diffracted matter wave is studied by considering a separation of the Fresnel function in terms of geometrical optics and diffracted waves. The behavior of the matter wave which is the counterpart of a geometrical optics field is investigated. Then a confined particle in a one-dimensional infinite potential well is taken into account. One of the walls of the trap is remained at an initial time and the process of diffraction in time is formulated by using the information, obtained from the geometrical optics fields. Some numerical results are given. This paper proposes two original approaches. The first one is the application of the optical diffraction theory to quantum physics. This is the separation of the scattered field into geometric optics and diffracted wave components. The second novelty is the addition of the effects of both of the traveling waves, which compose the standing wave, to the scattering integral.