Quantum mechanics in phase space
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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
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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