The three-dimensional Kepler problem and the four-dimensional isotropic harmonic oscillator

G. F. Torres Del Castillo; A. López Ortega

The three-dimensional Kepler problem and the four-dimensional isotropic harmonic oscillator

G. F. Torres Del Castillo, A. López Ortega

Research output: Contribution to journal › Article › peer-review

Abstract

Making use of the fact that certain submanifolds of the phase space of the four-dimensional isotropic harmonic oscillator can be identified with the phase space of the Kepler problem with an interaction with the field of a magnetic monopole and a centrifugal potential if the energy is negative, the solution of this problem in classical and quantum mechanics is obtained. Similar results for the case where the energy is equal to zero are also given.

Original language	English
Pages (from-to)	1-8
Number of pages	8
Journal	Revista Mexicana de Fisica
Volume	45
Issue number	1
State	Published - Feb 1999
Externally published	Yes

Keywords

Kepler problem
Kustaanheimo-Stiefel transformation
Magnetic monopole

Cite this

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AB - Making use of the fact that certain submanifolds of the phase space of the four-dimensional isotropic harmonic oscillator can be identified with the phase space of the Kepler problem with an interaction with the field of a magnetic monopole and a centrifugal potential if the energy is negative, the solution of this problem in classical and quantum mechanics is obtained. Similar results for the case where the energy is equal to zero are also given.

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KW - Kustaanheimo-Stiefel transformation

KW - Magnetic monopole

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The three-dimensional Kepler problem and the four-dimensional isotropic harmonic oscillator

Abstract

Keywords

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