Abstract
We construct the invertible map of the spin-state density operator onto the quasiprobability distribution of three continuous variables. We discuss the connection of this map with two-mode electromagnetic-field oscillators. We give the inversion formula for the spin-density matrix in terms of the Hermite polynomials. We examine the connection of the map constructed with the spin-tomographic representation. We consider the problem of the magnetic-moment rotation in the magnetic field in the suggested representation of spin states.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
D. Harland, M. J. Everitt, K. Nemoto, et al., Phys. Rev. A, 86, 062117 (2012).
P. Jordan, Z. Phys., 94, 531 (1935).
J. Schwinger, in: L. C. Biedenharn and H. Van Dam (Eds.), Quantum Theory of Angular Momentum, Academic (1965).
L. C. Biedenharn and J. D. Louck, Angular Momentum in Quantum Physics, Addison-Wesley Publishing Company, Reading (1981).
S. Mancini, V. I. Manko, and P. Tombesi, Phys. Lett. A, 213, 1 (1996).
A. Ibort, V. I. Manko, G. Marmo, et al., Phys. Scr., 79, 065013 (2009).
J. Radon, Ber. Verh. Sachs. Akad., 69, 262 (1917).
E. P. Wigner, Phys. Rev., 40, 749 (1932).
V. V. Dodonov and V. I. Man’ko, Phys. Lett. A, 229, 335 (1997).
V. I. Man’ko and O. V. Man’ko, J. Exp. Theor. Phys., 85, 430 (1997).
S. N. Filippov and V. I. Man’ko, J. Russ. Laser Res., 31, 211 (2010).
R. L. Stratonovich, J. Exp. Theor. Phys., 4, 891 (1957).
O. V. Man’ko, V. I. Manko, G. Marmo, and P. Vitale, Phys. Lett. A, 360, 522 (2007).
O. V. Man’ko, V. I. Man’ko, and G. Marmo, J. Phys. A: Math. Gen., 35, 699 (2002).
V. I. Man’ko, G. Marmo, and P. Vitale, Phys. Lett. A, 334, 1 (2005).
R. J. Glauber, Phys. Rev. Lett., 10, 84 (1963).
E. C. G. Sudarshan, Phys. Rev. Lett., 10, 177 (1963).
K. Husimi, Proc. Phys. Math. Soc. Jpn, 22, 264 (1940).
S. N. Filippov and V. I. Man’ko, J. Russ. Laser Res., 30, 129 (2009).
I. W. Busbridge, J. London Math. Soc., 23, 135 (1948).
M. A. Man’ko and V. I. Man’ko, AIP Conf. Proc., 1488, 110 (2012).
J. M. Radcliffe, J. Phys. A: Gen. Phys., 4, 313 (1971).
M. O. Terra Cunha, V. I. Man’ko, and M. O. Scully, Found. Phys. Lett., 14, 103 (2001).
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Lemeshevskiy, D.B., Man’ko, V.I. Hermite Polynomial Representation of the Spin States. J Russ Laser Res 34, 175–184 (2013). https://doi.org/10.1007/s10946-013-9340-0
Received:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10946-013-9340-0