New application of noncanonical maps in quantum mechanics
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Publication:1612697
DOI10.1023/A:1016035210661zbMATH Open0996.81505arXivquant-ph/0109036WikidataQ57514627 ScholiaQ57514627MaRDI QIDQ1612697
Author name not available (Why is that?)
Publication date: 26 August 2002
Published in: (Search for Journal in Brave)
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.
Full work available at URL: https://arxiv.org/abs/quant-ph/0109036
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