Generalized WKB and Milne solutions to one-dimensional wave equations

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Abstract
Diverse semianalytical constructions of wave functions, approximate or exact, are combined through the introduction of novel concepts. These include representing wave functions by a mosaic of analytic functions of a phase variable φ, each of them adapted to the problem’s features over a restricted range of a coordinate x, and focusing the numerical effort on the metric relation between φ and x. This shift of attention from the wave function proper to metric relations is viewed as the essence of the Milne approach and of its WKB approximation. Illustrative examples are worked out and discussed.

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