相空间演化与不连续薛定谔波
Phase Space Evolution and Discontinuous Schrödinger Waves
摘要：
本文研究了在一种新光源下不连续波函数的薛定谔传播问题--时间上的衍射。结果表明，在相空间的演化映射诱导一组仿射变换不连续波包，产生类似的小波分析的扩展。这种转换被确定为衍射图案中的无穷小细节的原因。一个简单的情况下，一个演化映射，如SL（2）在一个二维相空间中，被证明产生一个无限的一组恒定概率的时空轨迹。轨迹出现在初始波的一个断点。
英文摘要：
The problem of Schrödinger 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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