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Texas A&M University
Mathematics

Analysis/PDE Reading Seminar

Date: October 17, 2017

Time: 4:00PM - 5:00PM

Location: BLOC 624

Speaker: Robert Rahm, TAMU

  

Title: Asymptotic density of eigenvalues for 1 dimensional Schroedinger operators

Abstract: Consider the Schr\odinger Equation -y''(x) + q(x)y(x) = \lambda y(x) on $[0,\infty)$. We will initially assume only that q is non-negative and increasing and \lim_{x\to\infty}q(x) = \infty but will later put some restrictive assumptions on it. We will discuss the asymptotic density of eigenvalues of the equation. In particular, if N(T) is the number of eigenvalues less than T$ we will show: N(T) = \int_{0}^{q^{-1}(T)}\{T-q(x)\}^{1/2}dx + o(1).