Phase Space Evolution and Discontinuous Schrödinger Waves

Details Phase Space Evolution and Discontinuous Schrödinger Waves Phase Space Evolution and Discontinuous Schrödinger Waves

2012-02-10

arxiv.org/abs/1202.2333v1

J. Phys.: Conf. Ser. 343 012106 (2012)

Physics

Quantum Physics

Presented at the conference QTS7, Prague 2011. 12 pages, 7 figures

Scientific paper

10.1088/1742-6596/343/1/012106

The problem of Schr\"odinger propagation of a discontinuous wavefunction -diffraction in time- is studied under a new light. It is shown that the evolution map in phase space induces a set of affine transformations on discontinuous wavepackets, generating expansions similar to those of wavelet analysis. Such transformations are identified as the cause for the infinitesimal details in diffraction patterns. A simple case of an evolution map, such as SL(2) in a two-dimensional phase space, is shown to produce an infinite set of space-time trajectories of constant probability. The trajectories emerge from a breaking point of the initial wave.

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