Samuel L Braunstein 1998 J. Phys. A: Math. Gen. 31 5767 doi:10.1088/0305-4470/31/27/007
Samuel L Braunstein
Show affiliationsUsing a surprising result for the Wronskian of solutions with a common factor we show that all of the linearly independent solutions of linear-homogeneous ODEs 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 quasiphases of the linearly independent ODE solutions and hence clarifies the structure of solutions to linear ODEs.
34A30 Linear equations and systems, general
81Q20 Semiclassical techniques including WKB and Maslov methods
Issue 27 (10 July 1998)
Received 29 October 1997
Samuel L Braunstein 1998 J. Phys. A: Math. Gen. 31 5767
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