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arXiv · 1202.2333

Phase Space Evolution and Discontinuous Schr\"odinger Waves

Emerson Sadurni
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Abstract

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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Emerson Sadurni. 2012-02-10. Phase Space Evolution and Discontinuous Schr\"odinger Waves. https://doi.org/10.1088/1742-6596/343/1/012106

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