AIMR Math Group Seminar #15



Date : Feb. 4th (Mon.) 14:00~15:00

Place:3C, AIMR Main Bldg., Katahira campus, Tohoku University

SpeakerDr. Hideki Inoue

Title : Topological Levinson’s theorem beyond finitely many bound states



Levinson’s theorem is a relation between the scattering part and the number of bound states of a quantum system. It has been originally established for a Schr\”dinger operator with a spherically symmetric potential by N. Levinson in 1949, and then generalized to several systems by many researchers on purely analytical basis. In 2007, J. Kellendonk and S. Richard gave a topological interpretations of this relation as an index theorem in scattering theory by using some C*-algebraic methods. In this talk, we study the following question for a specific Shr\”odinger operator on the half-line: what happens if infinitely many bound states are involved? This talk is based on a joint work with S. Richard.





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