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

References in corpus (1)

• Gauge Invariance and Unstable Particles

Cited by in corpus (6)

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• Quantum Coherence of Critical Unstable Two-Level Systems
• On masses of unstable particles and their antiparticles in the CPT-invariant system
• Quantum Instability for Mixed States
• Inclusive Decay Distributions of Coherent Two-body States
• Need the masses of unstable particles and their antiparticles be equal in the CPT--invariant system?