dorsal/arxiv
View SchemaWhat could have we been missing while Pauli's Theorem was in force?
| Authors | Eric A. Galapon |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/0303106 |
| URL | https://arxiv.org/abs/quant-ph/0303106 |
Abstract
Pauli's theorem asserts that the canonical commutation relation $[T,H]=iI$ only admits Hilbert space solutions that form a system of imprimitivities on the real line, so that only non-self-adjoint time operators exist in single Hilbert quantum mechanics. This, however, is contrary to the fact that there is a large class of solutions to $[T,H]=iI$, including self-adjoint time operator solutions for semibounded and discrete Hamiltonians. Consequently the theorem has brushed aside and downplayed the rest of the solution set of the time-energy canonical commutation relation.
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"abstract": "Pauli\u0027s theorem asserts that the canonical commutation relation $[T,H]=iI$\nonly admits Hilbert space solutions that form a system of imprimitivities on\nthe real line, so that only non-self-adjoint time operators exist in single\nHilbert quantum mechanics. This, however, is contrary to the fact that there is\na large class of solutions to $[T,H]=iI$, including self-adjoint time operator\nsolutions for semibounded and discrete Hamiltonians. Consequently the theorem\nhas brushed aside and downplayed the rest of the solution set of the\ntime-energy canonical commutation relation.",
"arxiv_id": "quant-ph/0303106",
"authors": [
"Eric A. Galapon"
],
"categories": [
"quant-ph",
"hep-th"
],
"title": "What could have we been missing while Pauli\u0027s Theorem was in force?",
"url": "https://arxiv.org/abs/quant-ph/0303106"
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