A lower bound for level spacings

We consider a single particle in a negative potential V: H = -Δ + V(x). A lower bound is found for the quantity ε{lunate}_Λ - ε{lunate}_∞, where ε{lunate}_∞ is the ground-state energy of H in all space and where ε{lunate}_Λ is the ground-state energy of H in a bounded domain Λ with Dirichlet (ψ = 0) boundary conditions. Our estimate for ε{lunate}_Λ - ε{lunate}_∞ involves only ε{lunate}_Λ and the volume, | Λ |, but does not depend upon V or upon the shape of Λ.