Geometrical Relations for Charged Particles in a Uniform Magnetic Field
作者:
D. M. Thomson,
期刊:
American Journal of Physics
(AIP Available online 1972)
卷期:
Volume 40,
issue 11
页码: 1673-1678
ISSN:0002-9505
年代: 1972
DOI:10.1119/1.1987010
出版商: American Association of Physics Teachers
数据来源: AIP
摘要:
By using appropriate gauge transformations one can develop quasiclassical wavefunctions for charged particles in a uniform magnetic field which have large amplitudes only in the neighborhood of classical Larmor orbits centered at arbitrary points in a plane perpendicular to the field. Pairs of such wavefunctions are not orthogonal to each other. Interesting geometrical relationships between these solutions and the degenerate orthonormal sets of wave-functions in a particular gauge can be found as a result of evaluating overlap integrals. This has been done for both the cylindrical and Landau gauges. In the cylindrical gauge certain of the orthonormal wavefunctions corresponding to different energies give identical probability distributions. Relationships between quantum and classical results, and the effect of the uncertainty principle are discussed.
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