Semi-groups and time operators for quantum unstable systems
Quantum Physics
2007-05-23 v1
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.
Cite
@article{arxiv.quant-ph/0410082,
title = {Semi-groups and time operators for quantum unstable systems},
author = {Maurice Courbage},
journal= {arXiv preprint arXiv:quant-ph/0410082},
year = {2007}
}