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The eigenvalue equation has been found for a Hamilton function in a formindependent of the choice of a potential. This paper proposes a modifiedFedosov construction on a flat symplectic manifold. Necessary and sufficientconditions for solutions of an eigenvalue equation to be Wigner functions ofpure states are presented. The 1--D harmonic oscillator eigenvalue equation inthe coordinates time and energy is solved. A perturbation theory based on thevariables time and energy is elaborated.

Eigenvalue equation for a 1--D Hamilton function in deformation quantization