Geodesic
Calculating means of quantum observables in the optical tomography representation
Teoretičeskaâ i matematičeskaâ fizika, Tome 171 (2012) no. 3, pp. 475-482 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

We introduce a dual map from the special class $\mathcal A$ of quantum observables $\hat a$ to a special class of generalized functions $a(X,\phi)$. The class $\mathcal A$ includes all symmetrized polynomials in the canonical variables $\hat q$ and $\hat p$.
Keywords: optical tomogram, mean quantum observable, dual map. 
@article{TMF_2012_171_3_a8,
     author = {G. G. Amosov and Ya. A. Korennoi and V. I. Man'ko},
     title = {Calculating means of quantum observables in the~optical tomography representation},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {475--482},
     year = {2012},
     volume = {171},
     number = {3},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_2012_171_3_a8/}
}
TY  - JOUR
AU  - G. G. Amosov
AU  - Ya. A. Korennoi
AU  - V. I. Man'ko
TI  - Calculating means of quantum observables in the optical tomography representation
JO  - Teoretičeskaâ i matematičeskaâ fizika
PY  - 2012
SP  - 475
EP  - 482
VL  - 171
IS  - 3
UR  - http://geodesic.mathdoc.fr/item/TMF_2012_171_3_a8/
LA  - ru
ID  - TMF_2012_171_3_a8
ER  - 
%0 Journal Article
%A G. G. Amosov
%A Ya. A. Korennoi
%A V. I. Man'ko
%T Calculating means of quantum observables in the optical tomography representation
%J Teoretičeskaâ i matematičeskaâ fizika
%D 2012
%P 475-482
%V 171
%N 3
%U http://geodesic.mathdoc.fr/item/TMF_2012_171_3_a8/
%G ru
%F TMF_2012_171_3_a8
G. G. Amosov; Ya. A. Korennoi; V. I. Man'ko. Calculating means of quantum observables in the optical tomography representation. Teoretičeskaâ i matematičeskaâ fizika, Tome 171 (2012) no. 3, pp. 475-482. http://geodesic.mathdoc.fr/item/TMF_2012_171_3_a8/

[1] E. Wigner, Phys. Rev., 40:5 (1932), 749–759 | DOI | Zbl

[2] J. E. Moyal, Proc. Cambridge Philos. Soc., 45:1 (1949), 99–124 | DOI | MR | Zbl

[3] J. Bertrand, P. Bertrand, Found. Phys., 17:4 (1987), 397–405 | DOI | MR

[4] K. Vogel, H. Risken, Phys. Rev. A, 40:5 (1989), 2847–2849 | DOI

[5] S. Mancini, V. I. Man'ko, P. Tombesi, Quant. Semiclass. Opt., 7:4 (1995), 615–623 | DOI

[6] G. M. d'Ariano, U. Leonhardt, H. Paul, Phys. Rev. A, 52:3 (1995), R1801–R1804 | DOI

[7] O. Man'ko, V. I. Man'ko, J. Russ. Las. Res., 18:5 (1997), 407–444 | DOI

[8] A. S. Kholevo, Veroyatnostnye i statisticheskie aspekty kvantovoi teorii, Nauka, M., 1980 | MR | Zbl