Collapse of Wave-Packet component Phases: A Dispersion Relation Treatment
Pp. 225-256 (32)
Kramers-Kronig or dispersion relations that arise from the analytic behavior
of electromagnetic and other classical waves are here adapted to quantum
waves. In the framework of theories that view the wave packet (wp) collapse
as a time-continuous process, we postulate analytic properties for the
component-amplitudes in a wp as functions of a complex time. We then construct
a model which embodies the removal of the non-selected components
in the aftermath of the measurement, to be ultimately followed by a thermalequilibrium
like superposition state of the system. Conjugate relations hold
between component-moduli and phases and these show that a non-selected
component (one that vanishes in the measurement) acquires within the duration
of the collapse a fast oscillating phase factor. Thus, by virtue of
mathematical properties, both phase-decoherence and amplitude-decay have
to occur in a collapse process, indifferently to the physical mechanism.
Department of Physics and Applied Mathematics, Soreq NRC, Yavne 81800, Israel.