Huygens-Fresnel-Kirchhoff construction for quantum propagators with application to diffraction in space and time

Abstract

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Comparison between two models of absorption of matter waves by a thin time-dependent barrier

“…The first approach, which we will refer to as the aperture function model (AFM), was originally devised in Refs. [19,20]. It is based on modeling the absorbing barrier by means of discontinuous time-dependent boundary conditions at x = 0, connecting the values of the wave function and its spatial derivative across the barrier.…”

Manipulating quantum wave packets via time-dependent absorption

“…(12) and (13) and Eqs. (16) and (17) to analyze several scenarios of WP engineering corresponding to specific forms of the aperture function χ τ .…”

“…when numerically evaluating the integrals in Eqs. (13) and (16), instead of the one given by Eq. (18).…”

Three-dimensional Quantum Slit Diffraction and Diffraction in Time

“…In [16] as well as in [18], the wave at the source is considered to be a monochromatic plane wave. Here we consider, as in [20], a localized wave packet (Gaussian), but we follow the method developed in [18] to find the general solution. To understand the difference between the localized wave packet versus plane wave, we notice that the phase of the wave is non-linear in space and in time (for one dimension ϕ t (x) = mx 2 2 t ) and so the coordinate and time of emission of the localized wave has to be taken into account (which is not the case for a plane wave since the phase is linear in time, ϕ t (x) = kx − k 2 t 2m ).…”