On the solution of Hill's equation using Milne's method
- 1 May 1991
- journal article
- Published by IOP Publishing in Journal of Physics A: General Physics
- Vol. 24 (9) , 2069-2081
- https://doi.org/10.1088/0305-4470/24/9/017
Abstract
Milne's method is applied to the Hill equation, i.e. the Schrodinger equation for a periodic one-dimensional potential. The method allows a compact discussion of the organization and parameter dependence of the stability bands as well as an efficient numerical computation of the band edges. As an example a class of potentials which show a transition from two to one minimum per period is studied numerically. Furthermore, periodic solutions of the Milne equation are discussed and constructed.Keywords
This publication has 20 references indexed in Scilit:
- A simple way to understand the origin of the electron band structureAmerican Journal of Physics, 1988
- Band structure of a periodic potential with two wells and two barriers per periodAmerican Journal of Physics, 1987
- Periodic functional determinantsJournal of Physics A: General Physics, 1985
- Demonstration of wave propagation in a periodic structureAmerican Journal of Physics, 1985
- Hill’s Equation with a Large PotentialSIAM Journal on Applied Mathematics, 1985
- Discriminant, transmission coefficient, and stability bands of Hill’s equationJournal of Mathematical Physics, 1984
- A new solvable one-dimensional crystal modelJournal of Physics A: General Physics, 1983
- Milne's differential equation and numerical solutions of the Schrodinger equation. I. Bound-state energies for single- and double-minimum potentialsJournal of Physics B: Atomic and Molecular Physics, 1981
- The band-structure of a one-dimensional, periodic system in a scaling limitAnnals of Physics, 1979
- The Numerical Determination of Characteristic NumbersPhysical Review B, 1930