dorsal/arxiv
View SchemaA new application of non-canonical maps in quantum mechanics
| Authors | Giampiero Esposito |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/0109036 |
| URL | https://arxiv.org/abs/quant-ph/0109036 |
| Journal | Int.J.Theor.Phys. 41 (2002) 1043-1052 |
Abstract
A proof is given that an invertible and a unitary operator can be used to reproduce the effect of a q-deformed commutator of annihilation and creation operators. In other words, the original annihilation and creation operators are mapped into new operators, not conjugate to each other, whose standard commutator equals the identity plus a correction proportional to the original number operator. The consistency condition for the existence of this new set of operators is derived, by exploiting the Stone theorem on 1-parameter unitary groups. The above scheme leads to modified equations of motion which do not preserve the properties of the original first-order set for annihilation and creation operators. Their relation with commutation relations is also studied.
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"abstract": "A proof is given that an invertible and a unitary operator can be used to\nreproduce the effect of a q-deformed commutator of annihilation and creation\noperators. In other words, the original annihilation and creation operators are\nmapped into new operators, not conjugate to each other, whose standard\ncommutator equals the identity plus a correction proportional to the original\nnumber operator. The consistency condition for the existence of this new set of\noperators is derived, by exploiting the Stone theorem on 1-parameter unitary\ngroups. The above scheme leads to modified equations of motion which do not\npreserve the properties of the original first-order set for annihilation and\ncreation operators. Their relation with commutation relations is also studied.",
"arxiv_id": "quant-ph/0109036",
"authors": [
"Giampiero Esposito"
],
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"quant-ph"
],
"journal_ref": "Int.J.Theor.Phys. 41 (2002) 1043-1052",
"title": "A new application of non-canonical maps in quantum mechanics",
"url": "https://arxiv.org/abs/quant-ph/0109036"
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