Duke Mathematical Journal

Schrödinger operators with many bound states

David Damanik and Christian Remling

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Consider the Schrödinger operators H±=-d2/dx2±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±

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Duke Math. J., Volume 136, Number 1 (2007), 51-80.

First available in Project Euclid: 4 December 2006

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Zentralblatt MATH identifier

Primary: 34L15: Eigenvalues, estimation of eigenvalues, upper and lower bounds 81Q10: Selfadjoint operator theory in quantum theory, including spectral analysis


Damanik, David; Remling, Christian. Schrödinger operators with many bound states. Duke Math. J. 136 (2007), no. 1, 51--80. doi:10.1215/S0012-7094-07-13612-3. https://projecteuclid.org/euclid.dmj/1165244879

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