Dissertation/Thesis Abstract

Eigenvalue Problem as a Divergent Series
by Pottish, Samuel, M.S., California State University, Long Beach, 2018, 49; 10837282
Abstract (Summary)

We solve a time-independent perturbation problem with two new numerical approximation methods and compare their results. The methods are to approximate the bound state energies of a given Hamiltonain. We also use two ”gold-standard” methods to find the bound state energies of the Hamiltonian, being the Fredholm determinant and LAPACK. These will serve as a reference point for the two new approximation methods we will test. The new methods are divergent power series in λ and their stability and speed are tested for various values of the series order N. We found that a continued fractions method with quadruple-precision is the most stable in finding the bound state energies.

Indexing (document details)
Advisor: Papp, Zoltan
Commitee: Gu, Jiyeong, Jaikumar, Prashanth
School: California State University, Long Beach
Department: Physics and Astronomy
School Location: United States -- California
Source: MAI 58/02M(E), Masters Abstracts International
Subjects: Computational physics, Quantum physics, Physics, Particle physics
Keywords: Computational, Fortran, Matrix, Particle, Physics, Quantum
Publication Number: 10837282
ISBN: 9780438464803
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