Schr��dinger operators with many bound states (original) (raw)

Abstract

Abstract Consider the Schr��dinger operators $ H_ {\ pm}=-d^ 2/dx^ 2\ pm V (x) .Wepresentamethodforestimatingthepotentialintermsofthenegativeeigenvaluesoftheseoperators.AmongtheapplicationsareinverseLieb−Thirringinequalitiesandseveralsharpresultsconcerningthespectralpropertiesof. 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 .Wepresentamethodforestimatingthepotentialintermsofthenegativeeigenvaluesoftheseoperators.AmongtheapplicationsareinverseLieb−Thirringinequalitiesandseveralsharpresultsconcerningthespectralpropertiesof H_ {\ pm} $

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