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Journal of Mathematical Physics

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

Akira Yoshioka, Kiyotaka Ii

Published Jun 1, 1990• 4 citations
Publisher

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.

DOI
10.1063/1.528725

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