Geodesic
Self-adjoint phase operator
Teoretičeskaâ i matematičeskaâ fizika, Tome 38 (1979) no. 1, pp. 58-70 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

Quantization of action-angle variables is discussed. A self-adjoint phase operator is constructed for the harmonic oscillator, and some of its properties are investigated. The relative phase operator for two independent oscillators is described. Examples of a self-adjoint phase operator are given for reducible Weyl systems. 
@article{TMF_1979_38_1_a5,
     author = {A. L. Alimov and E. V. Damaskinsky},
     title = {Self-adjoint phase operator},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {58--70},
     year = {1979},
     volume = {38},
     number = {1},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_1979_38_1_a5/}
}
TY  - JOUR
AU  - A. L. Alimov
AU  - E. V. Damaskinsky
TI  - Self-adjoint phase operator
JO  - Teoretičeskaâ i matematičeskaâ fizika
PY  - 1979
SP  - 58
EP  - 70
VL  - 38
IS  - 1
UR  - http://geodesic.mathdoc.fr/item/TMF_1979_38_1_a5/
LA  - ru
ID  - TMF_1979_38_1_a5
ER  - 
%0 Journal Article
%A A. L. Alimov
%A E. V. Damaskinsky
%T Self-adjoint phase operator
%J Teoretičeskaâ i matematičeskaâ fizika
%D 1979
%P 58-70
%V 38
%N 1
%U http://geodesic.mathdoc.fr/item/TMF_1979_38_1_a5/
%G ru
%F TMF_1979_38_1_a5
A. L. Alimov; E. V. Damaskinsky. Self-adjoint phase operator. Teoretičeskaâ i matematičeskaâ fizika, Tome 38 (1979) no. 1, pp. 58-70. http://geodesic.mathdoc.fr/item/TMF_1979_38_1_a5/

[1] P. Carruthers, M. M. Nieto, Rev. Mod. Phys., 40:2 (1968), 411 ; Kogerentnye sostoyaniya v kvantovoi teorii, Sb. statei, NFF, no. 1, «Mir», 1972, 71–146 | DOI | MR

[2] A. S. Davydov, Kvantovaya mekhanika, Fizmatgiz, 1963 ; А. И. Базь, Я. Б. Зельдович, А. М. Переломов, Рассеяние, реакции и распады в нерелятивистской квантовой механике, Физматгиз, 1971 | MR | MR | Zbl

[3] P. A. M. Dirac, Proc. Roy. Soc., A114 (1927), 243 | DOI | Zbl

[4] V. A. Fok, Raboty po kvantovoi teorii polya, LGU, 1957

[5] N. I. Akhiezer, I. M. Glazman, Teoriya lineinykh operatorov v gilbertovom prostranstve, Fizmatgiz, 1966 | MR

[6] P. Khalmosh, Gilbertovo prostranstvo v zadachakh, «Mir», 1970 | MR | Zbl

[7] H. C. Volkin, J. Math. Phys., 14:12 (1973), 1965 | DOI | MR

[8] L. Susskind, I. Glogower, Physics, 1:1 (1964), 49

[9] I. C. Garrison, J. Wong, J. Math. Phys., 11:8 (1970), 2243 | DOI | MR

[10] V. N. Popov, V. S. Yarunin, Vestn. LGU, 1973, no. 22, 7; Е. В. Дамаскинский, В. С. Ярунин, Изв. ВУЗов., сер. физика, 1978, No 6, 59 | MR

[11] J. M. Levy-Leblond, Ann. Phys., 101:1 (1976), 319 | DOI | MR | Zbl

[12] F. Rocca, M. Sirugue, Commun. Math. Phys., 34:2 (1973), 111 | DOI | MR

[13] J. Provost, F. Rocca, G. Vallee, Ann. Phys., 94:2 (1975), 307 ; J. Provost, F. Rocca, G. Vallee, M. Sirugue, J. Math. Phys., 15:12 (1974), 2079 | DOI | MR | DOI | MR

[14] Zh. Emkh, Algebraicheskie metody v statisticheskoi mekhanike i kvantovoi teorii polya, «Mir», 1976 ; C. R. Putnam, Commutation properties of Hilbert Space Operators and Related Topics, Springer, N. Y., 1967 | MR | MR | Zbl

[15] K. Gofman, Banakhovy prostranstva analiticheskikh funktsii, IL, 1963

[16] M. Rosenblum, Pacif. J. Math., 10:3 (1960), 987 ; Proc. AMS, 13:4 (1962), 590 ; Amer. J. Math., 87:3 (1965), 709 | DOI | MR | Zbl | DOI | MR | Zbl | DOI | MR | Zbl

[17] I. Sigal, Matematicheskie problemy relyativistskoi fiziki, «Mir», 1968 ; I. E. Segal, Dan. Math. Fyss. D. Medd. Vid. Selsk., 31:12 (1959), 3 | MR | MR

[18] O. I. Zavyalov, V. N. Sushko, TMF, 1:2 (1969), 153 ; Статистическая физика и квантовая теория поля, Сб., Физматгиз, 1973, 411 | MR | MR

[19] J. M. Chaiken, Ann. Phys., 42:1 (1976), 22 ; Commun. Math. Phys., 8:21 (1968), 164 | MR | DOI | MR | Zbl

[20] M. A. Naimark, Normirovannye koltsa, fizmatgiz, 1968 | MR

[21] A. A. Grib, E. V. Damaskinskii, V. M. Maksimov, UFN, 120:4 (1970), 587 | DOI

[22] K. Napiorhowski, W. Pusz, Rept. Math. Phys., 3:3 (1972), 221 | DOI | MR

[23] H. Araki, E. J. Woods, J. Math. Phys., 4:5 (1963), 637 | DOI | MR