A law of large numbers and a central limit theorem for the Schrödinger operator with zero-range potentials
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We consider the Schrödinger operator with zero-range potentials onN points of three-dimensional space, independently chosen according to a common distributionV(x). Under some assumptions we prove that, whenN goes to infinity, the sequence converges to a Schrödinger operator with an effective potential. The fluctuations around the limit operator are explicitly characterized.
Key wordsZero-range potentials law of large numbers effective potentials
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