Quantum mechanics in phase space

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Standard

Quantum mechanics in phase space. / Hansen, Frank.

I: Reports on Mathematical Physics, Bind 19, Nr. 3, 1984, s. 361-381.

Publikation: Bidrag til tidsskrift › Tidsskriftartikel › Forskning › fagfællebedømt

Harvard

Hansen, F 1984, 'Quantum mechanics in phase space', Reports on Mathematical Physics, bind 19, nr. 3, s. 361-381. https://doi.org/10.1016/0034-4877(84)90008-9

APA

Hansen, F. (1984). Quantum mechanics in phase space. Reports on Mathematical Physics, 19(3), 361-381. https://doi.org/10.1016/0034-4877(84)90008-9

Vancouver

Hansen F. Quantum mechanics in phase space. Reports on Mathematical Physics. 1984;19(3):361-381. https://doi.org/10.1016/0034-4877(84)90008-9

Author

Hansen, Frank. / Quantum mechanics in phase space. I: Reports on Mathematical Physics. 1984 ; Bind 19, Nr. 3. s. 361-381.

Bibtex

@article{d960ada074c611dbbee902004c4f4f50,
title = "Quantum mechanics in phase space",
abstract = "A reformulation of quantum mechanics for a finite system is given using twisted multiplication of functions on phase space and Tomita's theory of generalized Hilbert algebras. Quantization of a classical observable h is achieved when the twisted exponential Exp0(-h) is defined as a tempered distribution. We show that h is in the domain of a generalized Weyl map and define Exp0(-h) as a tempered distribution provided h satisfies a certain semi-boundedness condition. The condition given is linear in h; it coincides with usual boundedness from below if h depends only on one canonical variable. Generalized Weyl-Wigner maps related to the notion of Hamiltonian weight are studied and used in the formulation of a twisted spectral theory for functions on phase space. Some inequalities for Wigner functions on phase space are proven. A brief discussion of the classical limit obtained through dilations of the twisted structure is added",
author = "Frank Hansen",
year = "1984",
doi = "10.1016/0034-4877(84)90008-9",
language = "English",
volume = "19",
pages = "361--381",
journal = "Reports on Mathematical Physics",
issn = "0034-4877",
publisher = "Pergamon Press",
number = "3",

}

RIS

TY - JOUR

T1 - Quantum mechanics in phase space

AU - Hansen, Frank

PY - 1984

Y1 - 1984

N2 - A reformulation of quantum mechanics for a finite system is given using twisted multiplication of functions on phase space and Tomita's theory of generalized Hilbert algebras. Quantization of a classical observable h is achieved when the twisted exponential Exp0(-h) is defined as a tempered distribution. We show that h is in the domain of a generalized Weyl map and define Exp0(-h) as a tempered distribution provided h satisfies a certain semi-boundedness condition. The condition given is linear in h; it coincides with usual boundedness from below if h depends only on one canonical variable. Generalized Weyl-Wigner maps related to the notion of Hamiltonian weight are studied and used in the formulation of a twisted spectral theory for functions on phase space. Some inequalities for Wigner functions on phase space are proven. A brief discussion of the classical limit obtained through dilations of the twisted structure is added

AB - A reformulation of quantum mechanics for a finite system is given using twisted multiplication of functions on phase space and Tomita's theory of generalized Hilbert algebras. Quantization of a classical observable h is achieved when the twisted exponential Exp0(-h) is defined as a tempered distribution. We show that h is in the domain of a generalized Weyl map and define Exp0(-h) as a tempered distribution provided h satisfies a certain semi-boundedness condition. The condition given is linear in h; it coincides with usual boundedness from below if h depends only on one canonical variable. Generalized Weyl-Wigner maps related to the notion of Hamiltonian weight are studied and used in the formulation of a twisted spectral theory for functions on phase space. Some inequalities for Wigner functions on phase space are proven. A brief discussion of the classical limit obtained through dilations of the twisted structure is added

U2 - 10.1016/0034-4877(84)90008-9

DO - 10.1016/0034-4877(84)90008-9

M3 - Journal article

VL - 19

SP - 361

EP - 381

JO - Reports on Mathematical Physics

JF - Reports on Mathematical Physics

SN - 0034-4877

IS - 3

ER -

ID: 158020