75 research outputs found
Diffraction of wave packets in space and time
The phenomenon of wave packet diffraction in space and time is described. It
consists in a diffraction pattern whose spatial location progresses with time.
The pattern is produced by wave packet quantum scattering off an attractive or
repulsive time independent potential. An analytical formula for the pattern at
is derived both in one dimension and in three dimensions. The
condition for the pattern to exist is developed. The phenomenon is shown
numerically and analytically for the Dirac equation in one dimension also. An
experiment for the verification of the phenomenon is described and simulated
numerically.Comment: replaces quant-ph 0008077, 0008107, Journal of physics, A, in pres
Single and double slit scattering of wave packets
The scattering of wave packets from a single slit and a double slit with the
Schr\"odinger equation, is studied numerically and theoretically.
The phenomenon of diffraction of wave packets in space and time in the
backward region, previously found for barriers and wells, is encountered here
also.
A new phenomenon of forward diffraction that occurs only for packets thiner
than the slit, or slits, is calculated numerically as well as, in a theoretical
approximation to the problem. This diffraction occurs at the opposite end of
the usual diffraction phenomena with monochromatic waves.Comment: Latex format, 35 pages, 15 eps (some colored) figure
A theorem for the normalization of continuous spectrum stationary states
We present analytic formulae that simplify the evaluation of the
normalization of continuous spectrum stationary states in the one-dimensional
Schr\"odinger equation.Comment: Corrected and enlarged version with exampl
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