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

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

2004-06-29

arxiv.org/abs/quant-ph/0406217v1

Physical Review A, 60, 3, 1802-1810 (1999)

Physics

Quantum Physics

17 pages, 3 figures

Scientific paper

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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