Unitarity and the time evolution of quantum mechanical states.

The basic requirement that, in quantum theory, the time-evolution of any state is determined by the action of a unitary operator, is shown to be the underlying cause for certain “exact” results which have recently been reported about the time-dependence of transition rates in quantum theory. Departures from exponential decay, including the “Quantum Zeno Effect”, as well as a theorem by Khalfin about the ratio of reciprocal transition-rates, are shown to follow directly from such considerations. At sufficiently short times, unitarity requires that reciprocity must hold, independent of whether T -invariance is valid. If T -invariance does not hold, unitarity restricts the form of possible time-dependence of reciprocity ratios. E-mail address: [email protected] E-mail address: [email protected]