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Journal of Mathematical Physics

Integral Approximations in Potential Scattering

Philip B. Burt, Forrest James Woods

Published Nov 1, 1971• 1 citation
Publisher

Abstract

A development of the scattering amplitude in potential scattering which is based upon replacing a smooth potential by a sequence of potential steps is given. The Schrödinger equation is solved exactly in each interval over which the potential is constant and by matching boundary conditions an expression relating the coefficients of two linearly independent solutions at small radius to those at large radius is found. From this the scattering amplitude is calculated. The limits of validity are found to be dependent upon the value of the expression (r/2)ddrln(2mℏ2[E−V]). Limiting cases of the amplitude are shown to be a modified WKB approximation and the Born approximation. A particular application to the Yukawa potential is discussed. The discussion is restricted to attractive potentials.

DOI
10.1063/1.1665531

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