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Discrete self-adjointness and quantum dynamics. Travel times

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JOURNAL OF MATHEMATICAL PHYSICS
卷 62, 期 1, 页码 -

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AIP Publishing
DOI: 10.1063/5.0021565

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In this paper, a discrete derivative is used to introduce a time operator for non-relativistic quantum systems with point spectrum. The symmetry requirement on the time operator leads to well-defined time values related to the dynamics of discrete quantum systems. Travel times between hits with the walls for the quantum particle in a box model are found, suggesting a classical analog of time eigenstates, and classical analogs for the Woods-Saxon potential are also proposed.
We use a discrete derivative to introduce a time operator for non-relativistic quantum systems with point spectrum. The symmetry requirement on the time operator leads to well-defined time values related to the dynamics of discrete quantum systems. As an illustration, we find travel times between hits with the walls for the quantum particle in a box model. These times suggest a classical analog of time eigenstates. We also briefly consider the Woods-Saxon potential and propose classical analogs for it.

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