Geometric quantisation of the MIC-Kepler problem

Mladenov, Iväılo M.; Tsanov, Vasil

doi:10.1088/0305-4470/20/17/020

Cited by 47 publications

(27 citation statements)

References 15 publications

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“…Thus, such a clear and natural, at the first glance, explanation of the origin of MICZ-term is not quite correct. On the other hand, this term can be obtained both on classical and quantum level when one reduce the four-dimensional isotropic oscillator with the aid of so-called Kustaanheimo-Stiefel transformations [4]. The shape of the classical trajectories of the MICZ-Kepler system coincides with these of the ordinary Coulomb one, however in contrast to the latter the orbital plane are non-orthogonal to the angular momentum vector.…”

Section: Introductionmentioning

confidence: 99%

Two-center quantum MICZ–Kepler system and the Zeeman effect in the charge–dyon system

Bellucci

Ohanyan

2008

Physics Letters A

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Communicated by P.R. HollandThe quantum two-center MICZ-Kepler system is considered in the limit when one of the interaction centers is situated at infinity, which leads to homogeneous electric and magnetic fields appearing in the system. The emerging system admits separation of variables in the Schrödinger equation and is integrable at the classical level. The first order corrections to the unperturbed spectrum of the ordinary MICZ-Kepler system are calculated. Particularly, the linear Zeeman effect and effects of MICZ-terms are analyzed. The possible realizations of the system in some quantum dots are considered.

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Section: Introductionmentioning

confidence: 99%

Two-center quantum MICZ–Kepler system and the Zeeman effect in the charge–dyon system

Bellucci

Ohanyan

2008

Physics Letters A

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“…The MIC-Kepler system has been worked out from different points of view in Refs. [12,13,14,15,16]. At s = 0, Eq.…”

Section: Introductionmentioning

confidence: 99%

Spheroidal analysis of the generalized MIC-Kepler system

Mardoyan

2005

Phys. Atom. Nuclei

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This paper deals with the dynamical system that generalizes the MIC-Kepler system. It is shown that the Schr\"{o}dinger equation for this generalized MIC-Kepler system can be separated in prolate spheroidal coordinates. The coefficients of the interbasis expansions between three bases (spherical, parabolic and spheroidal) are studied in detail. It is found that the coefficients for this expansion of the parabolic basis in terms of the spherical basis, and vice-versa, can be expresses through the Clebsch-Gordan coefficients for the group SU(2) analytically continued to real values of their arguments. The coefficients for the expansions of the prolate spheroidal basis in terms of the spherical and parabolic bases are proved to satisfy three-term recursion relations.Comment: 12 page

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“…Probably, first time it was pointed out by Zwanziger [1] an Schwinger [3]. Notice, also, that this term yields, when we treat to obtain the MICZ-Kepler system, similar to the Coulomb system, from the four-dimensional oscillator [5]. Let us mention, in this respect, that the Schroedinger equation for the MICZ-Kepler system is equivalent to the Schroedinger equation for the system of two well-separated BPS monopoles/dyons (which possesses the Coulomb symmetry) [6].…”

Section: Introductionmentioning

confidence: 83%