dorsal/arxiv
View SchemaSelf-adjoint Time Operator is the Rule for Discrete Semibounded Hamiltonians
| Authors | Eric A. Galapon |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/0111061 |
| URL | https://arxiv.org/abs/quant-ph/0111061 |
| DOI | 10.1098/rspa.2002.0992 |
| Journal | Proc. R. Soc. Lond. A 487 (2002) 2671 |
Abstract
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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"abstract": "We prove explicitly that to every discrete, semibounded Hamiltonian with\nconstant degeneracy and with finite sum of the squares of the reciprocal of its\neigenvalues and whose eigenvectors span the entire Hilbert space there exists a\ncharacteristic self-adjoint time operator which is canonically conjugate to the\nHamiltonian in a dense subspace of the Hilbert space. Moreover, we show that\neach characteristic time operator generates an uncountable class of self-\nadjoint operators canonically conjugate with the same Hamiltonian in the same\ndense subspace.",
"arxiv_id": "quant-ph/0111061",
"authors": [
"Eric A. Galapon"
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"doi": "10.1098/rspa.2002.0992",
"journal_ref": "Proc. R. Soc. Lond. A 487 (2002) 2671",
"title": "Self-adjoint Time Operator is the Rule for Discrete Semibounded Hamiltonians",
"url": "https://arxiv.org/abs/quant-ph/0111061"
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