Quantum wave packet propagation

N. A. Ivanov, V. V. Skalozub

Brian K. Kendrick

Brian K. Kendrick

Chyi-Lung Lin

We discuss the propagation dynamics of nonspreading wave packets. We decompose the Hamiltonian into two parts. The first part is such that wave packets is its instantaneous eigenstate and is therefore irrelevant to the propagation of the packet. The second part is shown to be the effective Hamiltonian governing the motion of the packet both classically and quantum mechanically. Thus, analogous to Ehrenfest's theorem, nonspreading wave packets offer another view point directly connecting quantum mechanics and classical mechanics. This analysis also works for non-square-integrable packets, such as Airy packets.

Dipankar Home, A. S. Majumdar, A. Matzkin

An analytical treatment of a propagating wave packet incident on a transient barrier reveals a counterintuitive quantum mechanical effect in which, for a particular time interval, the time-varying transmission probability {\it exceeds} (`superarrival') that for the free propagation of the wave packet. It is found that the speed with which the information about the barrier perturbation propagates across the wave packet can exceed the group velocity of the wave packet. An interesting implication of this effect regarding information transfer is analyzed by showing one-to-one correspondence between the strength of the barrier and the magnitude of `superarrival'.

John R. Merrill