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Necessary and Sufficient Conditions for a Hamiltonian with Discrete Eigenvalues to have Time Operators

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Abstract

We present new classes of time operators of a Hamiltonian H (a self-adjoint operator) with discrete eigenvalues which may be degenerate. Moreover we formulate necessary and sufficient conditions for H to have time operators, determining the general form of them. As corollaries, non-existence theorems of time operators for some classes of H are derived.

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  1. Department of Mathematics, Hokkaido University, Sapporo, Hokkaido, 060-0810, Japan

    Asao Arai

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  1. Asao Arai
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Correspondence to Asao Arai.

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Arai, A. Necessary and Sufficient Conditions for a Hamiltonian with Discrete Eigenvalues to have Time Operators. Lett Math Phys 87, 67–80 (2009). https://doi.org/10.1007/s11005-008-0286-z

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  • DOI: https://doi.org/10.1007/s11005-008-0286-z

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