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Self-Adjoint Time Operator Is the Rule for Discrete Semi-Bounded Hamiltonians

Eric A. Galapon
Proceedings: Mathematical, Physical and Engineering Sciences
Vol. 458, No. 2027 (Nov. 8, 2002), pp. 2671-2689
Published by: Royal Society
Stable URL: http://www.jstor.org/stable/3560026
Page Count: 19
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Self-Adjoint Time Operator Is the Rule for Discrete Semi-Bounded Hamiltonians
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Abstract

We prove explicitly that to every discrete semi-bounded Hamiltonian with constant degeneracy, and with a finite sum of the squares of the reciprocal of its eigenvalues and whose eigenvectors span the entire Hilbert space, there exists a characteristic self-adjoint time operator that is canonically conjugate to the Hamiltonian in a dense subspace of the Hilbert space. Moreover, we show that each characteristic time operator generates an uncountable class of self-adjoint operators canonically conjugate to the same Hamiltonian in the same dense subspace.

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