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.