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Generalized phase-integrals for linear homogeneous ODEs

Samuel L Braunstein

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Using 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.


PACS

03.65.Ge Solutions of wave equations: bound states

02.30.Hq Ordinary differential equations

MSC

34A30 Linear equations and systems, general

81Q20 Semiclassical techniques including WKB and Maslov methods

81Q05 Closed and approximate solutions to the Schrödinger, Dirac, Klein-Gordon and other quantum-mechanical equations

Subjects

Mathematical physics

Quantum information and quantum mechanics

Dates

Issue 27 (10 July 1998)

Received 29 October 1997



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