Article

Letters in Mathematical Physics

, Volume 85, Issue 2, pp 173-183

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

  • Maurice De GossonAffiliated withFakultät für Mathematik, NuHAG, Universität Wien Email author 
  • , Franz LuefAffiliated withFakultät für Mathematik, NuHAG, Universität Wien

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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.

Mathematics Subject Classification (2000)

47G30 81S10

Keywords

Moyal product star-genvalue equation Wigner transform Weyl operator.