Generic Short-Time Propagation of Sharp-Boundaries Wave Packets

Abstract

A general solution to the "shutter" problem is presented. The propagation of an arbitrary initially bounded wavefunction 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 ($t\ll 2m{x}^2/\hslash$, where $x$ is the distance to the boundaries) the wavefunction propagation depends only on the wavefunction's values (or its derivatives) at the boundaries of the region. Finally, we generalize these findings to a non-singular wavefunction (i.e., for wavepackets with finite-width boundaries) and suggest an experimental verification.

8 pages, 5 figures

References in corpus (4)

• Attosecond double-slit experiment
• Equivalence between the real time Feynman histories and the quantum shutter approaches for the "passage time" in tunneling
• Ultra-fast propagation of Schrödinger waves in absorbing media
• Hyperfine Spectroscopy of Optically Trapped Atoms

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