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SOME THRESHOLD SPECTRAL PROBLEMS OFSCHRODINGER OPERATORS

Abstract : THIS PHD THESIS DEALS WITH SOME SPECTRAL PROBLEMS OF SCHRODINGER OPERATORS. WE FIRST CONSIDER THE SEMI-CLASSICAL LIMIT OF THE NUMBER OF BOUND STATES OF UNIQUE TWO-CLUSTER N-BODY SCHRODINGER OPERATOR. THEN WE USE DIRICHLET-NEUMANN BRACKET TO GET SEMI-CLASSICAL LIMIT OF RIESZ MEANS OF THE DISCRETE EIGENVALUES OF N-BODY SCHR¨ODINGER OPERATOR. THE EFFECTIVE POTENTIAL OF N-BODY SCHRODINGER OPERATOR WITH COULOMB POTENTIAL IS ALSO CONSIDERED AND WE FIND THAT THE EFFECTIVE POTENTIAL HAS CRITICAL DECAY AT INFINITY. THUS, THE SCHRODINGER OPERATOR WITH CRITICAL POTENTIAL IS STUDIED IN THIS THESIS. WE STUDY THE COUPLING CONSTANT THRESHOLD OF SCHRODINGER OPERATOR WITH CRITICAL POTENTIAL AND THE ASYMPTOTIC EXPANSION OF RESOLVENT OF SCHRODINGER OPERATOR WITH CRITICAL POTENTIAL. WE USE THAT EXPANSION TO STUDY LOW-ENERGY ASYMPTOTICS OF DERIVATIVE OF SPECTRAL SHIFT FUNCTION FOR PERTURBATION WITH CRITICAL DECAY. AFTER THAT, WE USE THIS RESULT AND THE KNOWN RESULT FOR HIGH-ENERGY ASYMPTOTIC EXPANSION OF SPECTRAL SHIFT FUNCTION TO OBTAIN THE LEVINSON THEOREM.
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https://tel.archives-ouvertes.fr/tel-00403679
Contributor : Xiaoyao Jia <>
Submitted on : Monday, August 17, 2009 - 12:58:06 AM
Last modification on : Monday, March 25, 2019 - 4:52:05 PM
Long-term archiving on: : Thursday, September 23, 2010 - 5:43:58 PM

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  • HAL Id : tel-00403679, version 3

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Xiaoyao Jia. SOME THRESHOLD SPECTRAL PROBLEMS OFSCHRODINGER OPERATORS. Mathematics [math]. Université de Nantes, 2009. English. ⟨tel-00403679v3⟩

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