PHASE-INTEGRAL TREATMENT OF WAVE REFLECTION BY REAL POTENTIALS

Approximate analytical expressions for the wave reflexion amplitude for transmission above one-dimensional real smooth and slowly varying potentials in the absence of classical turning points are obtained in two different ways by means of the phase-integral method developed by N. Froman and P. O. Froman. The wave reflexion is shown to be governed by the complex transition points for the problem. The great accuracy of the formulae obtained, as well as their respective ranges of applicability, is illustrated by applying them, up to the eleventh order phase-integral approximation, to an exactly solvable model, for which the potential represents a monotonic step. © 1979, Cambridge Philosophical Society. All rights reserved.