Anuj, you better be more specific. There are plenty problem/situations where temporal behavior of a system is described by equations isomorphous to a regular spatial diffraction. The latter is also a huge field, and the simplest (often used in laser physics and nonlinear optics for the last 50 years) is a so called paraxial approximation whose eigenmodes are Gaussian beams. Similar equations often appear in the quantum mechanics and the theory of optical pulses in optical fibers. In quantum mechanics it is simply Scroedinger equation, which is isomorphous to paraxial approximation of electrodynamics. It is well known connection. So, do your study and formulate a very specific question; you don't want somebody else to do your homework for you, do you?:-)

I was reading Monshinsky, M., Phys Rev., 84, 525 (1951) and Caslev Brukner et al., Phys. Rev. A, Vol. 56, No. 5, 1997. Just trying to understand the similarity between regular spatial diffraction produced by single slit and the one that might be produced by a shutter in time (slit in time).

Anju, OK, to look into similarities, find out a so called paraxial wave wave equation (in any book on lasers, e. g. in Amnon Yariv's or Joseph Goodman's books, or any other source avalable to you; e. g. look into " Helmholtz equation" at Wikipedia) that describes a diffraction of light beam whose width "a" is larger than it wavelength "lambda". It is a partial differential equation, with the first partial derivative in the direction "z" of the beam propagation, and second order derivatives -- in the lateral dimensions. Its auto-model solutions are Gaussian beams, which are the main players in the theory of diffraction used these days in many areas of optics. Now, replace "z" coordinate by time "t", and properly rescale the coefficients of the equation, and you'll get a Schroedinger equation with a potential "U" being a rescaled profile of dielectric constant if it is space-dependent. In the simplest case whereby it isn't space-dependent, one have a "temporal_diffraction" in the first case, and "spatial_diffraction" in the second case. This connection is known in physics from 1930-ties.

An example of "temporal_diffraction" is a classical problem of how a spatially-limited quantum wave packet disperses in time if no confining potential is present. The solution is exactly the same as the one for a smooth single-slit spacial diffraction of light. In my course on quantum mechanics I give my students both of these solutions almost in a-back-to-back fashion. Similar "temporal_diffraction" problem exists in optics when considering a time-spreading of a limited pulse in a fiber with dispersion (or a plane wave in a medium with dispersion).

An interesting problem arises with "time_diffraction" of a quantum package in a confined potential, which results in the so called "quantum carpets", see e.g. at web-site

http://psi.ece.jhu.edu/~kaplan/PUBL/journ.html

papers #106 and #108 and later papers.

A very interesting process is brought up when both "temporal" and "spatial" diffraction play together (as e. g. in diffraction of very short, sub-cycle pulses), see paper #104 on the list of publications.

Hope this helps. -- Alex Kaplan

Thanks Alex. Reading your work.