03-76 Mihai Stoiciu
An estimate for the number of bound states of the Schrodinger operator in two dimensions (26K, AMSTeX) Feb 27, 03
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Abstract. For the Schrodinger operator $-\Delta + V$ on $\R^2$ let $N(V)$ be the number of bound states. One obtains the following estimate: $$N(V) \leq 1 + \int_{\R^2}\int_{\R^2} |V(x)| |V(y)| |C_1 \ln |x-y| + C_2|^2 dxdy$$ where $C_1 = -\frac{1}{2\pi}$ and $C_2 = \frac{\ln 2 - \gamma}{2 \pi}$ ($\gamma$ is the Euler constant). This estimate holds for all potentials for which the previous integral is finite.

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