This work was supported in part by the Oregon High Technology/Education Consortium, and by the California Microelectronics Innovation and Computer Research Opportunities (MICRO) Program.
Physical Review A
Linear differential equations, Mathematical analysis, Hill's equation -- Solution
A second-order linear differential equation with continuous periodic coefficients is solved exactly in terms of elementary functions. Equations of this type arise commonly in several areas of physics, and the solutions may find practical applications. As an illustration, the results are applied to the problem of an electron in a one-dimensional periodic potential.
Casperson, L. W. (1984). Solvable Hill equation. Physical Review A (General Physics), 30 (5), 2749-2751.