The spectral bound of Schrodinger operators
Let V : RN → [0, ∞] be a measurable function, and λ > 0 be a parameter. We consider the behaviour of the spectral bound of the operator 1/2Δ - λV as a function of λ. In particular, we give a formula for the limiting value as λ → ∞, in terms of the integrals of V over subsets of RN on which th...
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| Format: | Journal article |
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1996
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| Summary: | Let V : RN → [0, ∞] be a measurable function, and λ > 0 be a parameter. We consider the behaviour of the spectral bound of the operator 1/2Δ - λV as a function of λ. In particular, we give a formula for the limiting value as λ → ∞, in terms of the integrals of V over subsets of RN on which the Laplacian with Dirichlet boundary conditions has prescribed values. We also consider the question whether this limiting value is attained for finite λ. © 1996 Kluwer Academic Publishers. |
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