Europhys. Lett.
Volume 72, Number 3, November 2005
Page(s) 341 - 347
Section General
Published online 05 October 2005
Europhys. Lett., 72 (3), pp. 341-347 (2005)
DOI: 10.1209/epl/i2005-10264-2

Generic short-time propagation of sharp-boundaries wave packets

E. Granot1 and A. Marchewka2

1  Department of Electrical and Electronics Engineering College of Judea and Samaria - Ariel, Israel
2  Kibbutzim College of Education, Ramat-Aviv - 104 Namir Road 69978 Tel-Aviv, Israel

received 12 August 2005; accepted in final form 15 September 2005
published online 5 October 2005

A general solution to the "shutter" problem is presented. The propagation of an arbitrary initially bounded wave function is investigated, and the general solution for any such function is formulated. It is shown that the exact solution can be written as an expression that depends only on the values of the function (and its derivatives) at the boundaries. In particular, it is shown that at short times ( $t\ll 2mx^2/\hbar $, where x is the distance to the boundaries) the wave function propagation depends only on the wave function's values (or its derivatives) at the boundaries of the region. Finally, we generalize these findings to a non-singular wave function (i.e., for wave packets with finite-width boundaries) and suggest an experimental verification.

03.75.-b - Matter waves.
03.65.-w - Quantum mechanics.
03.65.Ge - Solutions of wave equations: bound states.

© EDP Sciences 2005