Self-adjoint Time Operator is the Rule for Discrete Semibounded Hamiltonians

Details Self-adjoint Time Operator is the Rule for Discrete Semibounded Hamiltonians Self-adjoint Time Operator is the Rule for Discrete Semibounded Hamiltonians

2001-11-10

arxiv.org/abs/quant-ph/0111061v2

Proc. R. Soc. Lond. A 487 (2002) 2671

Physics

Quantum Physics

accepted for publication in the Proceedings of the Royal Society of London A

Scientific paper

10.1098/rspa.2002.0992

We prove explicitly that to every discrete, semibounded Hamiltonian with constant degeneracy and with 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 which 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 with the same Hamiltonian in the same dense subspace.

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