Abstract
It is shown that time and entropy operators may exist as superoperators in the framework of the Liouville space provided that the Hamiltonian has an unbounded absolutely continuous spectrum. In this case the Liouville operator has uniform infinite multiplicity and thus the time operator may exist. A general proof of the Heisenberg uncertainty relation between time and energy is derived from the existence of this time operator.
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Courbage, M. On necessary and sufficient conditions for the existence of time and entropy operators in quantum mechanics. Lett Math Phys 4, 425–432 (1980). https://doi.org/10.1007/BF00943427
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DOI: https://doi.org/10.1007/BF00943427