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Condition for a bivariate normal probability distribution in phase space to be a quantum state

(1992) PHYSICAL REVIEW A. 46(9). p.5385-5388
Author
Organization
Abstract
In order that a bivariate normal probability distribution in phase space with variances sigma(q), sigma(p) and covariance sigma(q,p) may correspond to a Wigner distribution of a pure or a mixed state, it is n and sufficient that Heisenberg's uncertainty relation in Schrodinger form sigma(q)sigma(p)-sigma(q,p)2 greater-than-or-equal-to HBAR2/4 should be satisfied. The diagonalization of the corresponding density matrix entails a correspondence between the statistical and the physical properties of temperature-dependent oscillator states; the expansion of the density matrix into coherent states allows a physical interpretation in phase space.
Keywords
MECHANICS, GAUSSIAN-WIGNER DISTRIBUTIONS

Citation

Please use this url to cite or link to this publication:

Chicago
Kruger, Jan. 1992. “Condition for a Bivariate Normal Probability Distribution in Phase Space to Be a Quantum State.” Physical Review A 46 (9): 5385–5388.
APA
Kruger, Jan. (1992). Condition for a bivariate normal probability distribution in phase space to be a quantum state. PHYSICAL REVIEW A, 46(9), 5385–5388.
Vancouver
1.
Kruger J. Condition for a bivariate normal probability distribution in phase space to be a quantum state. PHYSICAL REVIEW A. 1992;46(9):5385–8.
MLA
Kruger, Jan. “Condition for a Bivariate Normal Probability Distribution in Phase Space to Be a Quantum State.” PHYSICAL REVIEW A 46.9 (1992): 5385–5388. Print.
@article{207256,
  abstract     = {In order that a bivariate normal probability distribution in phase space with variances sigma(q), sigma(p) and covariance sigma(q,p) may correspond to a Wigner distribution of a pure or a mixed state, it is n and sufficient that Heisenberg's uncertainty relation in Schrodinger form sigma(q)sigma(p)-sigma(q,p)2 greater-than-or-equal-to HBAR2/4 should be satisfied. The diagonalization of the corresponding density matrix entails a correspondence between the statistical and the physical properties of temperature-dependent oscillator states; the expansion of the density matrix into coherent states allows a physical interpretation in phase space.},
  author       = {Kruger, Jan},
  issn         = {1050-2947},
  journal      = {PHYSICAL REVIEW A},
  keyword      = {MECHANICS,GAUSSIAN-WIGNER DISTRIBUTIONS},
  language     = {eng},
  number       = {9},
  pages        = {5385--5388},
  title        = {Condition for a bivariate normal probability distribution in phase space to be a quantum state},
  url          = {http://dx.doi.org/10.1103/PhysRevA.46.5385},
  volume       = {46},
  year         = {1992},
}

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