Algebra with polynomial commutation relations for the Zeeman effect in the Coulomb-Dirac field

被引:0
作者
M. V. Karasev
E. M. Novikova
机构
[1] Moscow Institute of Electronics and Mathematics,
来源
Theoretical and Mathematical Physics | 2005年 / 142卷
关键词
integrable systems; Dirac monopole; nonlinear commutation relations; coherent states; asymptotic behavior of spectrum;
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摘要
We consider a model of particle motion in the field of an electromagnetic monopole (in the Coulomb-Dirac field) perturbed by homogeneous and inhomogeneous electric fields. After quantum averaging, we obtain an integrable system whose Hamiltonian can be expressed in terms of the generators of an algebra with polynomial commutation relations. We construct the irreducible representations of this algebra and its hypergeometric coherent states. We use these states to represent the eigenfunctions of the original problem in terms of the solutions of the model ordinary differential equation. We also present the asymptotic approximations of the eigenvalues in the leading term of the perturbation theory, where the degeneration of the spectrum is removed completely.
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页码:109 / 127
页数:18
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