Probability Representation of Quantum Observables and Quantum States

Vladimir N. Chernega1, О. В. Манько1, Vladimir I. Man’ko1
1Lebedev Physical Institute, Russian Academy of Sciences, Leninskii Prospect 53, Moscow, 119991, Russia

Tóm tắt

Từ khóa


Tài liệu tham khảo

E. Schrödinger, Ann. Phys. (Liepzig), 79, 489 (1926).

L. D. Landau, Z. Phys., 45, 430 (1927).

J. von Neumann, Nach. Ges. Wiss. Göttingen, 11, 245 (1927).

P. Dirac, The Principles of Quantum Mechanics, Oxford University Press (1930).

G. Esposito, G. Marmo, G. Miele, and E. C. G. Sudarshan, Advanced Concepts in Quantum Mechanics, Cambridge University Press, UK (2015).

G. Esposito, G. Marmo, and E. C. G. Sudarshan, From Classical to Quantum Mechanics: An Introduction to the Formalism, Foundations and Applications, Cambridge University Press (2004).

E. Wigner, Phys. Rev., 40, 749 (1932).

K. Husimi, Proc. Phys. Math. Soc. Jpn, 23, 264 (1940).

Y. Kano, J. Math. Phys., 6, 1913 (1986).

R. J. Glauber, Phys. Rev. Lett., 10, 84 (1963).

E. C. G. Sudarshan, Phys. Rev. Lett, 10, 84 (1963).

S. Mancini, V. I. Man’ko, and P. Tombesi, Phys. Lett. A, 213, 1 (1996).

J. Radon, Berichte Schsische Akademie der Wissenschaften, 29, 262, Leipzig (1917).

J. Bertrand and P. Bertrand, Found. Phys., 17, 397 (1989).

K. Vogel and H. Risken, Phys. Rev. A, 40, 2847 (1989).

D. T. Smithey, M. Beck, M. G. Raymer, and A. Faridani, Phys. Rev. Lett., 70, 1244 (1993).

V. V. Dodonov and V. I. Man’ko, Phys. Lett. A, 239, 335 (1997).

V. I. Man’ko and O. V. Man’ko, J. Exp. Theor. Phys., 85, 430 (1997).

O. V. Man’ko, in: B. Gruber and M. Ramek (Eds.), Proceedings of the International Conference “Symmetries in Science X” (Bregenz, Austria, 1997), Plenum Press, New York (1998), p. 207.

G. M. D’Ariano, L. Maccone, and M. Paini, J. Opt. B: Quantum Semiclass. Opt., 5, 77 (2003).

S. Weigert, Phys. Rev. Lett., 84, 802 (2000).

J.-P. Amiet and S. Weigert, J. Opt. B: Quantum Semiclass. Opt., 1, L5 (1999).

S. N. Filippov and V. I. Man’ko, Phys. Scr., 83, 058101 (2011).

S. N. Filippov and V. I. Man’ko, J. Russ. Laser Res., 32, 56 (2011).

A. Ibort, V. I. Man’ko, G. Marmo, et al., Phys. Scr., 79, 065013 (2009).

O. V. Man’ko, V. I. Man’ko, and G. Marmo, Phys. Scr., 62, 446 (2000).

M. Asorey, P. Facchi, V. I. Man’ko, et al., Phys. Rev. A, 76, 012117 (2007).

M. Asorey, P. Facchi, V. I. Man’ko, et al., Phys. Rev. A, 77, 042115 (2008).

O. V. Man’ko, V. I. Man’ko, G. Marmo, et al., Phys. Lett. A, 357, 255 (2006).

O. V. Man’ko and V. I. Man’ko, J. Russ. Laser Res., 18, 407(1997).

A. B. Klimov, O. V. Man’ko, V. I. Man’ko, et al., J. Phys. A: Math. Gen., 35, 6101 (2002).

O. V. Man’ko, in: Proceedings of the Wigner Centennial Conference (Pecs, Hungary, 2002), The Official Electronic Proceedings, paper 30; Acta Physica Hungarica A, Series Heavy Ion Physics, 19/3-4, 313 (2004).

V. N. Chernega and O. V. Man’ko, Phys. Scr., 30, 074052 (2015).

M. A. Man’ko, V. I. Man’ko, G. Marmo, et al., Nuovo Cimento C, 36, 163 (2013).

O. V. Man’ko, V. I. Man’ko, and G. Marmo, J. Phys. A: Math. Gen., 35, 699 (2002).

O. V. Man’ko, V. I.Man’ko, and G.Marmo, “Tomographic map within the framework of star-product quantization,” in: Proceedings of the Conference “Quantum Theory and Symmetries” (Krakow, 2001), World Scietific (2002), p. 126.

O. V. Man’ko and V. N. Chernega, JETP Lett., 97, 557(2013).

O. V. Manko, Phys. Scr., T135, 014004 (2009).

S. V. Kuznetsov, O. V. Man’ko, and N. V. Tcherniega, J. Opt. B: Quantum Semiclass. Opt., 5, S503 (2003).

R. L. Stratonovich, J. Exp. Theor. Phys., 5, 1206 (1957).

O. V. Man’ko, V. I. Man’ko, G. Marmo, and P. Vitale, Phys. Lett. A, 360, 522 (2007).

F. Lizzi and P. Vitale, SIGMA, 10, 36 (2014).

V. I. Man’ko, G. Marmo, F. Ventriglia, and P. Vitale, J. Phys. A: Math. Theor., 50, 335402 (2017).

V. N. Chernega, O. V. Man’ko, and V. I. Man’ko, J. Russ. Laser Res., 38, 141 (2017).