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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.

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Authors and Affiliations

  1. Fakultät für Mathematik, NuHAG, Universität Wien, Nordbergstrasse 15, 1090, Vienna, Austria

    Maurice De Gosson & Franz Luef

Authors
  1. Maurice De Gosson
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  2. Franz Luef
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Correspondence to Maurice De Gosson.

Additional information

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.

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Gosson, M.D., Luef, F. A New Approach to the \({\ast}\) -Genvalue Equation. Lett Math Phys 85, 173–183 (2008). https://doi.org/10.1007/s11005-008-0261-8

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  • DOI: https://doi.org/10.1007/s11005-008-0261-8

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