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Letters in Mathematical Physics

, Volume 85, Issue 2–3, pp 173–183 | Cite as

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

  • Maurice De Gosson
  • Franz Luef
Article

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.

Mathematics Subject Classification (2000)

47G30 81S10 

Keywords

Moyal product star-genvalue equation Wigner transform Weyl operator. 

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Copyright information

© Springer 2008

Authors and Affiliations

  1. 1.Fakultät für Mathematik, NuHAGUniversität WienViennaAustria

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