Algorithms for estimating spectral density functions for periodic potentials on the half line
Numerical Analysis
2013-03-26 v1
Abstract
For Hill's equation on [0,infinity) we prove new characterizations of the spectral function rho(lambda) and the spectral density function f(lambda) based on analysis involving a companion system of first order differential equations in [6,7]. A numerical algorithm is derived and implemented based on coefficient approximation. Results for several examples, including the Mathieu equation, are presented.
Cite
@article{arxiv.1303.5878,
title = {Algorithms for estimating spectral density functions for periodic potentials on the half line},
author = {Charles Fulton and David Pearson and Steven Pruess},
journal= {arXiv preprint arXiv:1303.5878},
year = {2013}
}