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 that 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. © 1996 The American Physical Society.