Scattering properties for a pair of Schrödinger type operators on cylindrical domains

Michael Melgaard

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We give sufficient conditions for the discreteness of the spectrum of differential operators of the form $A u = - △ u + (\nabla F, \nabla u)$ in $L_{μ}^{2} (R^{n})$ where $d μ (x) = e^{- F (x)} d x$ and for Schrödinger operators in $L^{2} (R^{n})$ . Our conditions are also necessary in the case of polynomial coefficients.