Coulomb–Kepler problem and the harmonic oscillator
作者:
Augustine C. Chen,
期刊:
American Journal of Physics
(AIP Available online 1987)
卷期:
Volume 55,
issue 3
页码: 250-252
ISSN:0002-9505
年代: 1987
DOI:10.1119/1.15196
出版商: American Association of Physics Teachers
关键词: HARMONIC OSCILLATORS;ANGULAR MOMENTUM;COUPLING;KEPLER LAWS;COULOMB FIELD;CLASSICAL MECHANICS;TRANSFORMATIONS
数据来源: AIP
摘要:
The three‐dimensional Coulomb–Kepler problem is shown to be equivalent to a pair of coupled two‐dimensional harmonic oscillators with the same angular momentum in classical mechanics by means of a Kustaanheimo–Stiefel transformation of coordinates and velocities. The constraint condition inherent in the transformation is shown to be related to the Runge–Lenz vector. The relationship between the action variables of the two systems is discussed. The equivalence is seen to result in the separability of the problem in parabolic coordinates.
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