On the Hartree–Fock scheme for a pair of adjoint operators
A generalization of the Hartree–Fock scheme for an arbitrary linear operator—and its adjoint—is derived by using the bivariational principle. It is shown that, if the system operator...
A generalization of the Hartree–Fock scheme for an arbitrary linear operator—and its adjoint—is derived by using the bivariational principle. It is shown that, if the system operator...
A characteristic function approach to the discrete spectrum of electrically charged particles
The purpose of this article is to obtain a scalar function the zeros of which give the discrete energy values for a system of electrically charged particles. The relation between the serial expansion ...
The purpose of this article is to obtain a scalar function the zeros of which give the discrete energy values for a system of electrically charged particles. The relation between the serial expansion ...
When is the Wigner function of multidimensional systems nonnegative?
J. Math. Phys. 24, 97 (1983); doi:10.1063/1.525607
Issue Date: January 1983
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It is shown that, for systems with an arbitrary number of degrees of freedom, a necessary and sufficient condition for the Wigner function to be nonnegative is that the corresponding state wavefunction is the exponential of a quadratic form. This result generalizes the one obtained by Hudson [Rep. Math. Phys. 6, 249 (1974)] for one-dimensional systems.
Journal of Mathematical Physics is copyrighted by The American Institute of Physics.
| History: | Received 24 February 1981; accepted 18 September 1981 |
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http://link.aip.org/link/?JMAPAQ/24/97/1 |
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BibSonomy
KEYWORDS and PACS
one&minus,
dimensional systems,
wave functions,
wigner theory,
probability,
distribution,
space,
gauss function,
many&minus,
dimensional calculations
- 03.65.Bz
Classical and quantum physics: mechanics and fields Quantum theory quantum mechanics Foundations, theory of measurement, miscellaneous theories - 03.65.Ca
Classical and quantum physics: mechanics and fields Quantum theory quantum mechanics Formalism - 05.30.Ch
Statistical physics and thermodynamics Quantum statistical mechanics Quantum ensemble theory - YEAR: 1983
PUBLICATION DATA
0022-2488 (print)
1089-7658 (online)
AIP
REFERENCES (12)
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- E. Wigner,
Phys. Rev. 40, 749–759 (1932 ). - J. E. Moyal,
Proc. Cambridge Philos. Soc. 45, 99–124 (1949 ). - S. De Groot, La transformation de Weyl et la fonction de Wigner: une forme alternative de la mécanique quantique (Les Presses de l'Université de Montréal, 1974).
- R. L. Hudson,
Rep. Math. Phys. 6, 249–252 (1974 ). - C. Piquet,
C. R. Acad. Sci. Paris A 279, 107–109 (1974 ). - R. J. Glauber,
Phys. Rev. 131, 2766–2788 (1963 ). - J. C. T. Pool, J. Math. Phys. 7, 66–76 (1966).
- B. A. Fuks, Introduction to the Theory of Analytic Functions of Several Complex Variables (American Mathematical Society, Providence, R. I., 1963).
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- C. Piquet (private communication).
- W. Feller, Introduction to probability theory and its applications (Wiley, New York, 1966), Chap. XV, Sec. 8, pp. 498–499.
