Generalized phase-integrals for linear homogeneous ODEs

## Generalized phase-integrals for linear homogeneous ODEs

• Braunstein, S. L. (1998): Journal of Physics A, 5767-5773. (PDF)

ABSTRACT: Using a surprising result for the Wronskian of solutions with a common factor we show that {\it all\/} the linearly independent solutions of linear homogeneous ordinary differential equations have a simple form in a generalized phase-integral representation. This allows the generalization of WKB-like expansions to higher-order differential equations in a way that extends the usual phase-integral methods. This work clarifies the internal structure of phase-integral representations as being discrete transforms over the quasi-phases of the linearly independent ODE solutions and hence clarifies the structure of solutions to linear ODEs.