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Showing 1 to 6 of 6 for “"Schrodinger Operators"”.
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Krein's identity and trace formulas for half-line Schrodinger operators
We consider self-adjoint extensions of the minimal operator generated by the differential expression $\cL = - d^2/dx^2+V$ on the half-line $[0,\infty)$, where $V$ is a real-valued function integrable with respect to the weight $1+x$. The self-adjoint extensions are of Schr\"odinger-type and form a …
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Diagonalization of 1-D Schrodinger Operators with Piecewise Constant Potentials
<p>In today's world our lives are very layered. My research is meant to adapt current inefficient numerical methods to more accurately model the complex situations we encounter. This project focuses on a specific equation that is used to model sound speed in the ocean. As depth increases, the sound …
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Vague convergence of spectral shift functions for periodic restrictions of one-dimensional Schrodinger operators
… with self-adjoint one-dimensional Schr\"odinger operators on intervals of the form $(-\ell,\ell)$ with periodic boundary conditions to the full-line spectral shift function in the infinite volume limit $\ell\to \infty$. The approach employed relies on the use of a Krein-type resolvent identity to …
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Heat trace and heat content asymptotics for Schrodinger Operators of stable processes/fractional Laplacians
<p>Let <em>V</em> be a bounded and integrable potential over <strong>R</strong><em><sup>d</sup></em> and 0 < α ≤ 2. We show the existence of an asymptotic expansion by means of Fourier Transform techniques and probabilistic methods for the following quantities [special characters omitted] and …
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Dispersive estimates for the Schrödinger equation
Item withdrawn by Mark Zulauf (zulauf@illinois.edu) on 2010-06-30T12:54:50Z Item was in collections: University of Illinois Theses & Dissertations (ID: 1) No. of bitstreams: 1 Green_William.pdf: 999536 bytes, checksum: 87eb33f24c92fd62a4874b5db34bf8da (MD5)
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Two Random Multiplicative Processes: Multiplicative Cascades and Eigenvectors of the Random Schrodinger Operator
… of the one-dimensional discrete random Schrodinger operator. This is the Hamiltonian operator on the lattice of integers given by the discrete Laplacian plus an independent, identically distributed delta potential at each point. We restrict this operator to a finite box, pick an …