Asymptotics of reflectionless potentials

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Analytic reflectionless potentials 2() are constructed for the one-dimensional equation 2d2q/d2+2()q=0. Unlike generic potentials which reflect waves with amplitudes of order exp(-1/) as '0, these potentials have reflection coefficients which are identically 0. It is shown that in the reflectionless case the adiabatic perturbation or iteration does not converge absolutely or terminate at some order. Since exact integrability is less restrictive than having a reflectionless potential, the case studied also shows that integrability does not imply convergence of the approximation methods used.

Original languageEnglish (US)
Pages (from-to)2413-2416
Number of pages4
JournalPhysical review letters
Issue number16
StatePublished - 1992
Externally publishedYes

All Science Journal Classification (ASJC) codes

  • General Physics and Astronomy


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