Title page for ETD etd-12132002-163620


Type of Document Dissertation
Author Toloza, Julio Hugo
URN etd-12132002-163620
Title Exponentially Accurate Error Estimates of Quasiclassical Eigenvalues
Degree PhD
Department Physics
Advisory Committee
Advisor Name Title
Hagedorn, George A. Committee Chair
Chang, Lay Nam Committee Co-Chair
Klaus, Martin Committee Member
Kohler, Werner E. Committee Member
Schmittmann, Beate Committee Member
Keywords
  • exponentially accurate asymptotics
Date of Defense 2002-12-11
Availability unrestricted
Abstract
We study the behavior of truncated Rayleigh-Schröodinger series for the low-lying eigenvalues of the time-independent Schröodinger equation, when the Planck's constant is considered in the semiclassical limit.

Under certain hypotheses on the potential energy, we prove that, for any given small value of the Planck's constant, there is an optimal truncation of the series for the approximate eigenvalues, such that the difference between an approximate and actual eigenvalue is smaller than an exponentially small function of the Planck's constant. We also prove the analogous results concerning the eigenfunctions.

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