Unitarity and the Time Evolution of Quantum Mechanical Systems

Details Unitarity and the Time Evolution of Quantum Mechanical Systems Unitarity and the Time Evolution of Quantum Mechanical Systems

1995-09-20

arxiv.org/abs/hep-ph/9509349v1

Phys.Rev. A53 (1996) 66-69

Physics

High Energy Physics

High Energy Physics - Phenomenology

LaTeX, 10 pages

Scientific paper

10.1103/PhysRevA.53.66

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.

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