S. M. Chumakov, A. B. Klimov, K. B. Wolf, “Connection between two Wigner functions for spin systems,” Phys. Rev. A 61, 034101-1–034101-3 (2000).

[CrossRef]

N. M. Atakishiyev, S. M. Chumakov, K. B. Wolf, “Wigner distribution function for finite systems,” J. Math. Phys. 39, 6247–6261 (1998);S. M. Chumakov, A. Frank, K. B. Wolf, “Finite Kerr medium: macroscopic quantum superposition states and Wigner functions on the sphere,” Phys. Rev. A 60, 1817–1822 (1999).

[CrossRef]

L. M. Nieto, N. A. Atakishiyev, S. M. Chumakov, K. B. Wolf, “Wigner distribution function for Euclidean systems,” J. Phys. A 31, 3875–3895 (1998).

[CrossRef]

A. L. Rivera, N. M. Atakishiyev, S. M. Chumakov, K. B. Wolf, “Evolution under polynomial Hamiltonians in quantum and optical phase spaces,” Phys. Rev. A 55, 876–889 (1997).

[CrossRef]

K. B. Wolf, “Wigner distribution function for paraxial polychromatic optics,” Opt. Commun. 132, 343–352 (1996).

[CrossRef]

J. P. Dowling, G. S. Agarwal, W. P. Schleich, “Wigner distribution of a general angular momentum state: application to a collection of two-level atoms,” Phys. Rev. A 49, 4101–4109 (1994).

[CrossRef]
[PubMed]

J. C. Várilly, J. M. Garcia-Bondía, “The Moyal representation for spin,” Ann. Phys. (Paris) 190, 107–148 (1989);C. Brif, A. Mann, “Phase space formulation of quantum mechanics and quantum state reconstruction for physical systems with Lie-group symmetries,” Phys. Rev. A 59, 971–987 (1999).

[CrossRef]

G. S. Agarwal, “Relation between atomic coherent-state representation, state multipoles, and generalized phase-space distributions,” Phys. Rev. A 24, 2889–2896 (1981).

[CrossRef]

A. Lohmann, “The Wigner function and its optical production,” Opt. Commun. 42, 32–37 (1980).

A. Royer, “Wigner function as the expectation value of the parity operator,” Phys. Rev. A 15, 449–450 (1977).

[CrossRef]

F. T. Arecchi, E. Courtens, R. Gilmore, H. Thomas, “Atomic coherent states in quantum optics,” Phys. Rev. A 6, 2211–2237 (1972).

[CrossRef]

R. L. Stratonovich, “On distribution in representation space,” Sov. Phys. JETP 4, 891–898 (1957) [J. Exp. Theor. Phys. 31, 1012–1020 (1956)].

E. Inönü, E. P. Wigner, “On the contraction of groups and their representations,” Proc. Natl. Acad. Sci. USA 39, 510–524 (1953).

[CrossRef]
[PubMed]

J. E. Moyal, “Quantum mechanics as a statistical theory,” Proc. Cambridge Philos. Soc. 45, 99–124 (1949).

[CrossRef]

E. P. Wigner, “On the quantum correction for thermodynamic equilibrium,” Phys. Rev. 40, 749–759 (1932).

[CrossRef]

J. P. Dowling, G. S. Agarwal, W. P. Schleich, “Wigner distribution of a general angular momentum state: application to a collection of two-level atoms,” Phys. Rev. A 49, 4101–4109 (1994).

[CrossRef]
[PubMed]

G. S. Agarwal, “Relation between atomic coherent-state representation, state multipoles, and generalized phase-space distributions,” Phys. Rev. A 24, 2889–2896 (1981).

[CrossRef]

S. T. Ali, N. A. Atakishiyev, S. M. Chumakov, K. B. Wolf, “The Wigner function for general Lie groups and the wavelet transform,” Ann. Inst. Henri Poincaré Phys. Theor. (to be published).

J.-P. Amiet, S. Weigert, “Contracting the Wigner-kernel of a spin to the Wigner-kernel of a particle,” Phys. Rev. A (to be published).

F. T. Arecchi, E. Courtens, R. Gilmore, H. Thomas, “Atomic coherent states in quantum optics,” Phys. Rev. A 6, 2211–2237 (1972).

[CrossRef]

L. M. Nieto, N. A. Atakishiyev, S. M. Chumakov, K. B. Wolf, “Wigner distribution function for Euclidean systems,” J. Phys. A 31, 3875–3895 (1998).

[CrossRef]

S. T. Ali, N. A. Atakishiyev, S. M. Chumakov, K. B. Wolf, “The Wigner function for general Lie groups and the wavelet transform,” Ann. Inst. Henri Poincaré Phys. Theor. (to be published).

N. M. Atakishiyev, S. M. Chumakov, K. B. Wolf, “Wigner distribution function for finite systems,” J. Math. Phys. 39, 6247–6261 (1998);S. M. Chumakov, A. Frank, K. B. Wolf, “Finite Kerr medium: macroscopic quantum superposition states and Wigner functions on the sphere,” Phys. Rev. A 60, 1817–1822 (1999).

[CrossRef]

A. L. Rivera, N. M. Atakishiyev, S. M. Chumakov, K. B. Wolf, “Evolution under polynomial Hamiltonians in quantum and optical phase spaces,” Phys. Rev. A 55, 876–889 (1997).

[CrossRef]

S. M. Chumakov, A. B. Klimov, K. B. Wolf, “Connection between two Wigner functions for spin systems,” Phys. Rev. A 61, 034101-1–034101-3 (2000).

[CrossRef]

L. M. Nieto, N. A. Atakishiyev, S. M. Chumakov, K. B. Wolf, “Wigner distribution function for Euclidean systems,” J. Phys. A 31, 3875–3895 (1998).

[CrossRef]

N. M. Atakishiyev, S. M. Chumakov, K. B. Wolf, “Wigner distribution function for finite systems,” J. Math. Phys. 39, 6247–6261 (1998);S. M. Chumakov, A. Frank, K. B. Wolf, “Finite Kerr medium: macroscopic quantum superposition states and Wigner functions on the sphere,” Phys. Rev. A 60, 1817–1822 (1999).

[CrossRef]

A. L. Rivera, N. M. Atakishiyev, S. M. Chumakov, K. B. Wolf, “Evolution under polynomial Hamiltonians in quantum and optical phase spaces,” Phys. Rev. A 55, 876–889 (1997).

[CrossRef]

S. T. Ali, N. A. Atakishiyev, S. M. Chumakov, K. B. Wolf, “The Wigner function for general Lie groups and the wavelet transform,” Ann. Inst. Henri Poincaré Phys. Theor. (to be published).

F. T. Arecchi, E. Courtens, R. Gilmore, H. Thomas, “Atomic coherent states in quantum optics,” Phys. Rev. A 6, 2211–2237 (1972).

[CrossRef]

J. P. Dowling, G. S. Agarwal, W. P. Schleich, “Wigner distribution of a general angular momentum state: application to a collection of two-level atoms,” Phys. Rev. A 49, 4101–4109 (1994).

[CrossRef]
[PubMed]

A. Frank, P. Vansacker, Algebraic Methods in Molecular and Nuclear Structure (Wiley Interscience, New York, 1994).

J. C. Várilly, J. M. Garcia-Bondía, “The Moyal representation for spin,” Ann. Phys. (Paris) 190, 107–148 (1989);C. Brif, A. Mann, “Phase space formulation of quantum mechanics and quantum state reconstruction for physical systems with Lie-group symmetries,” Phys. Rev. A 59, 971–987 (1999).

[CrossRef]

F. T. Arecchi, E. Courtens, R. Gilmore, H. Thomas, “Atomic coherent states in quantum optics,” Phys. Rev. A 6, 2211–2237 (1972).

[CrossRef]

E. Inönü, E. P. Wigner, “On the contraction of groups and their representations,” Proc. Natl. Acad. Sci. USA 39, 510–524 (1953).

[CrossRef]
[PubMed]

D. A. Varshalovich, A. N. Moskalev, V. K. Khersonskı̌, Quantum Theory of Angular Momentum (World Scientific, Singapore, 1988).

S. M. Chumakov, A. B. Klimov, K. B. Wolf, “Connection between two Wigner functions for spin systems,” Phys. Rev. A 61, 034101-1–034101-3 (2000).

[CrossRef]

N. Ya. Vilenkin, A. U. Klimyk, Representations of Lie Groups and Special Functions (Kluwer Academic, Dordrecht, The Netherlands, 1991), Vol. 1.

A. Lohmann, “The Wigner function and its optical production,” Opt. Commun. 42, 32–37 (1980).

D. A. Varshalovich, A. N. Moskalev, V. K. Khersonskı̌, Quantum Theory of Angular Momentum (World Scientific, Singapore, 1988).

J. E. Moyal, “Quantum mechanics as a statistical theory,” Proc. Cambridge Philos. Soc. 45, 99–124 (1949).

[CrossRef]

L. M. Nieto, N. A. Atakishiyev, S. M. Chumakov, K. B. Wolf, “Wigner distribution function for Euclidean systems,” J. Phys. A 31, 3875–3895 (1998).

[CrossRef]

A. L. Rivera, N. M. Atakishiyev, S. M. Chumakov, K. B. Wolf, “Evolution under polynomial Hamiltonians in quantum and optical phase spaces,” Phys. Rev. A 55, 876–889 (1997).

[CrossRef]

A. Royer, “Wigner function as the expectation value of the parity operator,” Phys. Rev. A 15, 449–450 (1977).

[CrossRef]

J. P. Dowling, G. S. Agarwal, W. P. Schleich, “Wigner distribution of a general angular momentum state: application to a collection of two-level atoms,” Phys. Rev. A 49, 4101–4109 (1994).

[CrossRef]
[PubMed]

R. L. Stratonovich, “On distribution in representation space,” Sov. Phys. JETP 4, 891–898 (1957) [J. Exp. Theor. Phys. 31, 1012–1020 (1956)].

F. T. Arecchi, E. Courtens, R. Gilmore, H. Thomas, “Atomic coherent states in quantum optics,” Phys. Rev. A 6, 2211–2237 (1972).

[CrossRef]

A. Frank, P. Vansacker, Algebraic Methods in Molecular and Nuclear Structure (Wiley Interscience, New York, 1994).

J. C. Várilly, J. M. Garcia-Bondía, “The Moyal representation for spin,” Ann. Phys. (Paris) 190, 107–148 (1989);C. Brif, A. Mann, “Phase space formulation of quantum mechanics and quantum state reconstruction for physical systems with Lie-group symmetries,” Phys. Rev. A 59, 971–987 (1999).

[CrossRef]

D. A. Varshalovich, A. N. Moskalev, V. K. Khersonskı̌, Quantum Theory of Angular Momentum (World Scientific, Singapore, 1988).

J.-P. Amiet, S. Weigert, “Contracting the Wigner-kernel of a spin to the Wigner-kernel of a particle,” Phys. Rev. A (to be published).

E. Inönü, E. P. Wigner, “On the contraction of groups and their representations,” Proc. Natl. Acad. Sci. USA 39, 510–524 (1953).

[CrossRef]
[PubMed]

E. P. Wigner, “On the quantum correction for thermodynamic equilibrium,” Phys. Rev. 40, 749–759 (1932).

[CrossRef]

S. M. Chumakov, A. B. Klimov, K. B. Wolf, “Connection between two Wigner functions for spin systems,” Phys. Rev. A 61, 034101-1–034101-3 (2000).

[CrossRef]

K. B. Wolf, M. A. Alonso, G. W. Forbes, “Wigner function for Helmholtz wave fields,” J. Opt. Soc. Am. A 16, 2476–2487 (1999).

[CrossRef]

L. M. Nieto, N. A. Atakishiyev, S. M. Chumakov, K. B. Wolf, “Wigner distribution function for Euclidean systems,” J. Phys. A 31, 3875–3895 (1998).

[CrossRef]

N. M. Atakishiyev, S. M. Chumakov, K. B. Wolf, “Wigner distribution function for finite systems,” J. Math. Phys. 39, 6247–6261 (1998);S. M. Chumakov, A. Frank, K. B. Wolf, “Finite Kerr medium: macroscopic quantum superposition states and Wigner functions on the sphere,” Phys. Rev. A 60, 1817–1822 (1999).

[CrossRef]

A. L. Rivera, N. M. Atakishiyev, S. M. Chumakov, K. B. Wolf, “Evolution under polynomial Hamiltonians in quantum and optical phase spaces,” Phys. Rev. A 55, 876–889 (1997).

[CrossRef]

K. B. Wolf, “Wigner distribution function for paraxial polychromatic optics,” Opt. Commun. 132, 343–352 (1996).

[CrossRef]

S. T. Ali, N. A. Atakishiyev, S. M. Chumakov, K. B. Wolf, “The Wigner function for general Lie groups and the wavelet transform,” Ann. Inst. Henri Poincaré Phys. Theor. (to be published).

N. Ya. Vilenkin, A. U. Klimyk, Representations of Lie Groups and Special Functions (Kluwer Academic, Dordrecht, The Netherlands, 1991), Vol. 1.

J. C. Várilly, J. M. Garcia-Bondía, “The Moyal representation for spin,” Ann. Phys. (Paris) 190, 107–148 (1989);C. Brif, A. Mann, “Phase space formulation of quantum mechanics and quantum state reconstruction for physical systems with Lie-group symmetries,” Phys. Rev. A 59, 971–987 (1999).

[CrossRef]

N. M. Atakishiyev, S. M. Chumakov, K. B. Wolf, “Wigner distribution function for finite systems,” J. Math. Phys. 39, 6247–6261 (1998);S. M. Chumakov, A. Frank, K. B. Wolf, “Finite Kerr medium: macroscopic quantum superposition states and Wigner functions on the sphere,” Phys. Rev. A 60, 1817–1822 (1999).

[CrossRef]

L. M. Nieto, N. A. Atakishiyev, S. M. Chumakov, K. B. Wolf, “Wigner distribution function for Euclidean systems,” J. Phys. A 31, 3875–3895 (1998).

[CrossRef]

K. B. Wolf, “Wigner distribution function for paraxial polychromatic optics,” Opt. Commun. 132, 343–352 (1996).

[CrossRef]

A. Lohmann, “The Wigner function and its optical production,” Opt. Commun. 42, 32–37 (1980).

E. P. Wigner, “On the quantum correction for thermodynamic equilibrium,” Phys. Rev. 40, 749–759 (1932).

[CrossRef]

A. L. Rivera, N. M. Atakishiyev, S. M. Chumakov, K. B. Wolf, “Evolution under polynomial Hamiltonians in quantum and optical phase spaces,” Phys. Rev. A 55, 876–889 (1997).

[CrossRef]

A. Royer, “Wigner function as the expectation value of the parity operator,” Phys. Rev. A 15, 449–450 (1977).

[CrossRef]

J. P. Dowling, G. S. Agarwal, W. P. Schleich, “Wigner distribution of a general angular momentum state: application to a collection of two-level atoms,” Phys. Rev. A 49, 4101–4109 (1994).

[CrossRef]
[PubMed]

G. S. Agarwal, “Relation between atomic coherent-state representation, state multipoles, and generalized phase-space distributions,” Phys. Rev. A 24, 2889–2896 (1981).

[CrossRef]

S. M. Chumakov, A. B. Klimov, K. B. Wolf, “Connection between two Wigner functions for spin systems,” Phys. Rev. A 61, 034101-1–034101-3 (2000).

[CrossRef]

F. T. Arecchi, E. Courtens, R. Gilmore, H. Thomas, “Atomic coherent states in quantum optics,” Phys. Rev. A 6, 2211–2237 (1972).

[CrossRef]

J. E. Moyal, “Quantum mechanics as a statistical theory,” Proc. Cambridge Philos. Soc. 45, 99–124 (1949).

[CrossRef]

E. Inönü, E. P. Wigner, “On the contraction of groups and their representations,” Proc. Natl. Acad. Sci. USA 39, 510–524 (1953).

[CrossRef]
[PubMed]

R. L. Stratonovich, “On distribution in representation space,” Sov. Phys. JETP 4, 891–898 (1957) [J. Exp. Theor. Phys. 31, 1012–1020 (1956)].

A. Frank, P. Vansacker, Algebraic Methods in Molecular and Nuclear Structure (Wiley Interscience, New York, 1994).

J.-P. Amiet, S. Weigert, “Contracting the Wigner-kernel of a spin to the Wigner-kernel of a particle,” Phys. Rev. A (to be published).

D. A. Varshalovich, A. N. Moskalev, V. K. Khersonskı̌, Quantum Theory of Angular Momentum (World Scientific, Singapore, 1988).

S. T. Ali, N. A. Atakishiyev, S. M. Chumakov, K. B. Wolf, “The Wigner function for general Lie groups and the wavelet transform,” Ann. Inst. Henri Poincaré Phys. Theor. (to be published).

N. Ya. Vilenkin, A. U. Klimyk, Representations of Lie Groups and Special Functions (Kluwer Academic, Dordrecht, The Netherlands, 1991), Vol. 1.