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Medientyp:
E-Artikel
Titel:
Mathematical Aspects of the Weyl Correspondence
Beteiligte:
Pool, James C. T.
Erschienen:
AIP Publishing, 1966
Erschienen in:
Journal of Mathematical Physics, 7 (1966) 1, Seite 66-76
Sprache:
Englisch
DOI:
10.1063/1.1704817
ISSN:
0022-2488;
1089-7658
Entstehung:
Anmerkungen:
Beschreibung:
The Weyl correspondence between classical and quantum observables is rigorously formulated for a linear mechanical system with a finite number of degrees of freedom. A multiplication of functions and a *-operation are introduced to make the Hilbert space of Lebesgue square-integrable complex-valued functions on phase space into a H*-algebra. The Weyl correspondence is realized as a *-isomorphism f → W(f) of this H*-algebra onto the H*-algebra of Hilbert-Schmidt operators on the Hilbert space of Lebesgue square-integrable complex-valued functions on configuration space. Moreover, the kernel of W(f) is exhibited in terms of a Fourier-Plancherel transform of f. Elementary properties of the Wigner quasiprobability density function and its characteristic function are deduced and used to obtain these results.