, Volume 85, Issue 2-3, pp 173-183
Date: 16 Aug 2008

A New Approach to the \({\ast}\) -Genvalue Equation

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Abstract

We show that the eigenvalues and eigenfunctions of the star-genvalue equation can be completely expressed in terms of the corresponding eigenvalue problem for the quantum Hamiltonian. Our methods make use of a Weyl-type representation of the star-product and of the properties of the cross-Wigner transform, which appears as an intertwining operator.

M. de Gosson has been financed by the Austrian Research Agency FWF (Projekt “Symplectic Geometry and Applications to TFA and QM”, Projektnummer P20442-N13).
F. Luef has been supported by the European Union EUCETIFA grant MEXT-CT-2004-517154.