Motion on the n-dimensional ellipsoid under the influence of a harmonic force revisited

Details Motion on the n-dimensional ellipsoid under the influence of a harmonic force revisited Motion on the n-dimensional ellipsoid under the influence of a harmonic force revisited

2002-11-28

arxiv.org/abs/hep-th/0211273v1

J.Phys.A36:10159-10172,2003

Physics

High Energy Physics

High Energy Physics - Theory

Latex2e, 18 pages

Scientific paper

10.1088/0305-4470/36/40/003

The $n$ integrals in involution for the motion on the $n$-dimensional ellipsoid under the influence of a harmonic force are explicitly found. The classical separation of variables is given by the inverse momentum map. In the quantum case the Schr\"odinger equation separates into one-dimensional equations that coincide with those obtained from the classical separation of variables. We show that there is a more general orthogonal parametrisation of Jacobi type that depends on two arbitrary real parameters. Also if there is a certain relation between the spring constants and the ellipsoid semiaxes the motion under the influence of such a harmonic potential is equivalent to the free motion on the ellipsoid.

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