Liouville's Equation - Part Two - Eigenmodes of Harmonic Potentials

Details Liouville's Equation - Part Two - Eigenmodes of Harmonic Potentials Liouville's Equation - Part Two - Eigenmodes of Harmonic Potentials

Apr 1989

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1989a%26a...214...83s&link_type=abstract

Astronomy and Astrophysics, Vol. 214, NO.1/2/APR(II), P. 83, 1989

Astronomy and Astrophysics

Astrophysics

10

Scientific paper

Exact and complete set of eigenfunctions and eigenvalues of a harmonic potential are presented. The eigenfunctions constitute three distinct sequences of analytic, coanalytic, and non analytic functions in Z = p + iq, where (q, p) are phase space coordinates. Solutions are obtained by a pair of raising and lowering operators for Liouville's equation. Ellipsoidal, spheroidal and spherical potentials are discussed separately and in details.

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