Algorithms for estimating spectral density functions for periodic\n potentials on the half line

2013/03/23 by Charles T. Fulton, Fulton, Charles, D. B. Pearson +4
Computer Science · Mathematics · Physics and Astronomy · #FOS: Mathematics #Nonlinear Dynamics and Pattern Formation #Numerical Analysis #Numerical Analysis (math.NA) #Numerical methods for differential equations #Quantum chaos and dynamical systems

paper · pdf · doi:10.48550/arxiv.1303.5878

openalex publication_date 2013/03/23 · openalex created_date 2022/10/05 · openalex updated_date 2026/07/28

Abstract

For Hill's equation on [0,infinity) we prove new characterizations of the\nspectral function rho(lambda) and the spectral density function f(lambda) based\non analysis involving a companion system of first order differential equations\nin [6,7]. A numerical algorithm is derived and implemented based on coefficient\napproximation. Results for several examples, including the Mathieu equation,\nare presented.\n

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