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).