Semi-Groups and Time Operators for Quantum Unstable Systems
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We use spectral projections of time operator in the Liouville space for simple quantum scattering systems in order to define a space of unstable particle states evolving under a contractive semi-group. This space includes purely exponentially decaying states that correspond to complex eigenvalues of this semi-group. The construction provides a probabilistic interpretation of the resonant states characterized in terms of the Hardy class.
Keywordsquantum ustable system time operator semigroup time evolution Hardy spaces Liouville spaces
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