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arxiv: math-ph/0412091 · v1 · pith:AYY5EJRLnew · submitted 2004-12-26 · 🧮 math-ph · math.MP· math.SP

Schr\"odinger Operators with Many Bound States

classification 🧮 math-ph math.MPmath.SP
keywords operatorsodingerschrapplicationsboundconcerningconsidereigenvalues
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Consider the Schr\"odinger operators $H_{\pm}=-d^2/dx^2\pm V(x)$. We present a method for estimating the potential in terms of the negative eigenvalues of these operators. Among the applications are inverse Lieb-Thirring inequalities and several sharp results concerning the spectral properties of $H_{\pm}$.

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