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arXiv · quant-ph/0406217

Reciprocity between Moduli and Phases in Time-Dependent Wave-Functions

R. Englman·A. Yahalom·M. Baer
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Abstract

For time (t) dependent wave functions we derive rigorous conjugate relations between analytic decompositions (in the complex t-plane) of the phases and of the log moduli. We then show that reciprocity, taking the form of Kramers-Kronig integral relations (but in the time domain), holds between observable phases and moduli in several physically important instances. These include the nearly adiabatic (slowly varying) case, a class of cyclic wave-functions, wave packets and non-cyclic states in an "expanding potential". The results exhibit the interdependence of geometric-phases and related decay probabilities. Several known quantum mechanical theories possess the reciprocity property obtained in the paper.

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R. Englman, A. Yahalom, M. Baer. 2004-06-29. Reciprocity between Moduli and Phases in Time-Dependent Wave-Functions. https://arxiv.org/abs/quant-ph/0406217

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