A lower bound for level spacings |
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| Authors: | Elliott H Lieb Walter E Thirring |
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| Institution: | Departments of Mathematics and Physics, Princeton University, Princeton, New Jersey 08540 USA;Institut für Theoretische Physik, Universität Wien, Wien, Austria |
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| Abstract: | We consider a single particle in a negative potential V: H = ?Δ + V(x). A lower bound is found for the quantity ?Λ ? ?∞, where ?∞ is the ground-state energy of H in all space and where ?Λ is the ground-state energy of H in a bounded domain Λ with Dirichlet (ψ = 0) boundary conditions. Our estimate for ?Λ ? ?∞ involves only ?Λ and the volume, | Λ |, but does not depend upon V or upon the shape of Λ. |
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