On the spectral L{sub 2} conjecture, 3/2-Lieb-Thirring inequality and distributional potentials

Journal Article · Thu Dec 15 00:00:00 EST 2005 · Journal of Mathematical Physics

DOI:https://doi.org/10.1063/1.2142837· OSTI ID:20768698

Rybkin, Alexei ^[1]

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1. Department of Mathematical Sciences, University of Alaska, Fairbanks, P.O. Box 756660, Fairbanks, AK 99775 (United States)

Let H=-{partial_derivative}{sub x}{sup 2}+V(x) be a properly defined Schroedinger operator on L{sub 2}(R) with real potentials of the form V(x)=q(x)+p{sup '}(x) (the derivative is understood in the distributional sense) with some p,q set-membership sign L{sub 2}(R). We prove that the absolutely continuous spectrum of H fills (0,{infinity}) which was previously proven by Deift-Killip for V set-membership sign L{sub 2}(R). We also refine the 3/2-Lieb-Thirring inequality.

• OSTI ID: 20768698
• Journal Information: Journal of Mathematical Physics, Vol. 46, Issue 12; Other Information: DOI: 10.1063/1.2142837; (c) 2005 American Institute of Physics; Country of input: International Atomic Energy Agency (IAEA); ISSN 0022-2488
• Country of Publication: United States
• Language: English

Related Subjects

71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
INTEGRAL EQUATIONS
MATHEMATICAL OPERATORS
MATHEMATICAL SOLUTIONS
POTENTIALS
SCHROEDINGER EQUATION