Geodesic
Quasi-Classical Approximation of Monopole Harmonics
Matematičeskie zametki, Tome 114 (2023) no. 6, pp. 848-862.

Voir la notice de l'article provenant de la source Math-Net.Ru

Using the generalization of the multidimensional WKB method to magnetic Laplacians corresponding to monopoles, which we proposed earlier, we obtain explicit formulas for quasi-classical approximations of eigenfunctions for the Dirac monopole.
Keywords: quasi-classical approximation, magnetic Laplacian, magnetic monopole. 
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Yu. A. Kordyukov; I. A. Taimanov. Quasi-Classical Approximation of Monopole Harmonics. Matematičeskie zametki, Tome 114 (2023) no. 6, pp. 848-862. http://geodesic.mathdoc.fr/item/MZM_2023_114_6_a4/

[1] Yu. A. Kordyukov, I. A. Taimanov, “Kvaziklassicheskoe priblizhenie dlya magnitnykh monopolei”, UMN, 75:6 (456) (2020), 85–106 | DOI | MR | Zbl

[2] I. A. Taimanov, “Geometriya i kvaziklassicheskoe kvantovanie magnitnykh monopolei”, TMF, 2023 (to appear)

[3] V. P. Maslov, Teoriya vozmuschenii i asimptoticheskie metody, Izd-vo MGU, M., 1965 | MR

[4] V. P. Maslov, M. V. Fedoryuk, Kvaziklassicheskoe priblizhenie dlya uravnenii kvantovoi mekhaniki, Nauka, M., 1976 | MR

[5] A. Yu. Anikin, S. Yu. Dobrokhotov, V. E. Nazaikinskii, A. V. Tsvetkova, “Ravnomernaya asimptotika v vide funktsii Eiri dlya kvaziklassicheskikh svyazannykh sostoyanii v odnomernykh i radialno-simmetrichnykh zadachakh”, TMF, 201:3 (2019), 382–414 | DOI | MR

[6] S. Y. Dobrokhotov, A. A. Tolchennikov, “Keplerian trajectories and an asymptotic solution of the Schrödinger equation with repulsive Coulomb potential and localized right-hand side”, Russ. J. Math. Phys., 29:4 (2022), 456–466 | DOI | MR

[7] P. A. M. Dirak, “Kvantovannye singulyarnosti v elektromagnitnom pole”, Sobranie nauchnykh trudov, 2: Kvantovaya teoriya (nauchnye stati 1924–1947 gg.), Fizmatlit, M., 2003, 388–398 | DOI | MR

[8] I. Tamm, “Die verallgemeinerten Kugelfunktionen und die Wellenfunktionen eines Elektrons im Felde eines Magnetpoles”, Z. Phys., 3–4 (1931), 141–150 | DOI

[9] T. T. Wu, C. N. Yang, “Dirac monopole without strings: monopole harmonics”, Nuclear Phys. B, 107:3 (1976), 365–380 | DOI | MR

[10] S. Yu. Dobrokhotov, V. E. Nazaikinskii, A. I. Shafarevich, “Novye integralnye predstavleniya kanonicheskogo operatora Maslova v osobykh kartakh”, Izv. RAN. Ser. matem., 81:2 (2017), 53–96 | DOI | MR