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Semi-groups and time operators for quantum unstable systems

Maurice Courbage
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Abstract

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.

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Maurice Courbage. 2004-10-11. Semi-groups and time operators for quantum unstable systems. https://arxiv.org/abs/quant-ph/0410082

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