Discriminant, transmission coefficient, and stability bands of Hill’s equation

1 October 1984

journal article
research article
Published by AIP Publishing in Journal of Mathematical Physics

Vol. 25 (10) , 2903-2904
https://doi.org/10.1063/1.526036

Abstract

The discriminant Δ(k²) of Hill’s equation is shown to be related to the transmission coefficient T(k)e^iθ(k) of one period of the potential by Δ(k²)=[2/T(k)]cos[kπ+θ(k)]. This result is used to find the boundaries of the stability bands.

Keywords

HILL EQUATION
POTENTIALS
PERIODIC VARIATIONS
FLOQUET FUNCTION

This publication has 1 reference indexed in Scilit:

Hill’s Equation with a Large Potential
SIAM Journal on Applied Mathematics, 1985