An Estimate for the Number of Bound States of the Schrödinger Operator in Two Dimensions
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چکیده
For the Schrödinger operator −∆ + V on R2 let N(V ) be the number of bound states. One obtains the following estimate: N(V ) ≤ 1 + ∫ R2 ∫ R2 |V (x)| |V (y)| |C1 ln |x− y|+ C2| dx dy where C1 = − 1 2π and C2 = ln 2−γ 2π (γ is the Euler constant). This estimate holds for all potentials for which the previous integral is finite.
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تاریخ انتشار 2003