Unitarity and the Time Evolution of Quantum Mechanical Systems

Abstract

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.

LaTeX, 10 pages