The quantization condition in the presence of a magnetic field and quasiclassical eigenvalues of the Kepler problem with a centrifugal potential and Dirac’s monopole field
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引用次数: 5
Abstract
In the presence of a magnetic field, the Maslov quantization condition is not available in the original form. An alternative quantization condition is proposed with the aid of a principal U(1) bundle over a phase space and a connection whose curvature form is the charged symplectic form. By means of this quantization condition, quasiclassical eigenvalues of the Kepler problem with a centrifugal potential and Dirac’s monopole field are calculated, which turn out to coincide with the eigenvalues of the quantized problem.
期刊介绍：
Journal of Mathematical Physics, Analysis, Geometry (JMPAG) publishes original papers and reviews on the main subjects:
mathematical problems of modern physics;
complex analysis and its applications;
asymptotic problems of differential equations;
spectral theory including inverse problems and their applications;
geometry in large and differential geometry;
functional analysis, theory of representations, and operator algebras including ergodic theory.
The Journal aims at a broad readership of actively involved in scientific research and/or teaching at all levels scientists.
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