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

- Author
- Jan Kruger
- 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: http://hdl.handle.net/1854/LU-207256

- 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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