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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 phi, 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 phi 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.

Asymmetric resonance profiles observed in H atoms in a strong electric field are derived analytically. The most significant deviations from a Lorentzian line shape, H/sup F/ = ..gamma../(scre/sup 2/+..gamma../sup 2/), occur for resonances near the top of a potential barrier. Parametrization as a Fano profile is inappropriate. The line-shape formula, a Lorentzian with energy-dependent reduced width ..gamma../sub Q/(scre) = ln(1+Q(1-Q)/sup -1-s/cre)/ln(( 1-Q)/sup -1/), depends on a single asymmetry parameter Q (0