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

Englman, R.; Yahalom, A.; Baer, M.

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

Authors

Englman, R.

Yahalom, A.

Baer, M.

Description

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.
17 pages, 3 figures