Geodesic
Goryachev–Chaplygin top in quantum mechanics
Teoretičeskaâ i matematičeskaâ fizika, Tome 50 (1982) no. 3, pp. 402-409 
I. V. Komarov. Goryachev–Chaplygin top in quantum mechanics. Teoretičeskaâ i matematičeskaâ fizika, Tome 50 (1982) no. 3, pp. 402-409. http://geodesic.mathdoc.fr/item/TMF_1982_50_3_a9/
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     author = {I. V. Komarov},
     title = {Goryachev{\textendash}Chaplygin top in quantum mechanics},
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     pages = {402--409},
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     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_1982_50_3_a9/}
}
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Voir la notice de l'article provenant de la source Math-Net.Ru

The quantum analog of the Goryachev–Chaplygin top on the basis of the Euclidean group $E(3)$ is constructed. A representation of the generators of $E(3)$ by functions of two bosch creation and annihilation operators is considered, the problem taking on its most natural form in terms of these operators. For example, the finding of the spectrum of integrals in the Fock representation reduces to finding the eigenvalues of semi-infinite tridiagonal Jacobi matrices; the equations of motion acquire a particularly simple form.

[1] Gorr G. V., Kudryashova L. V., Stepanova L. A., Klassicheskie zadachi dinamiki tverdogo tela, Naukova dumka, Kiev, 1978 | MR

[2] Chaplygin S. A., Novyi sluchai vrascheniya tverdogo tela, podpertogo v odnoi tochke, Sobr. soch. t. I, Gostekhizdat, M., 1948, 118–124

[3] Komarov I. V., TMF, 47:1 (1981), 67–72 | MR

[4] Kozlov V. V., Metody kachestvennogo analiza v dinamike tverdogo tela, MGU, M., 1980 | MR

[5] Flashka H., Mc Laughlin D. W., Progr. Theor. Phys., 55:2 (1976), 438–456 | DOI | MR

[6] Malkin I. A., Manko V. I., Dinamicheskie simmetrii i kogerentnye sostoyaniya kvantovykh sistem, Nauka, M., 1979 | MR

[7] Sudarshan E. C. G., Mukunda N., Phys. Rev., D1:2 (1970), 571–589 | MR

[8] Györgyi G., Kövesi-Domokos S., Nuovo Cim., B58:1 (1968), 191–200 | DOI

[9] Komarov I. V., Ponomarev L. I., Slavyanov S. Yu., Sferoidalnye i kulonovskie sferoidalnye funktsii, Nauka, M., 1976 | MR | Zbl

[10] Braun P. A., TMF, 37:3 (1978), 355–370 | MR

[11] Faddeev L. D., Yakubovskii O. A., Lektsii po kvantovoi mekhanike dlya studentov-matematikov, LGU, L., 1980 | MR