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

Petre Dita
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Abstract

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 Schrödinger 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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Petre Dita. 2002-11-28. Motion on the n-dimensional ellipsoid under the influence of a harmonic force revisited. https://doi.org/10.1088/0305-4470%2F36%2F40%2F003

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