Configuration properties of S-matrix and time-delay for potentials decaying like |χ|−α, α >1

Mohapatra, A. ; Sinha, Kalyan B. ; Amerin, W. O. (1992) Configuration properties of S-matrix and time-delay for potentials decaying like |χ|−α, α >1 Annales de l'Institut Henri Poincare, Section A - Physique Théorique, 57 (1). pp. 89-113. ISSN 0020-2339

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Official URL: http://archive.numdam.org/ARCHIVE/AIHPA/AIHPA_1992...

Abstract

The time-delay in a simple quantum mechanical scattering process is a simple mechanical scattering process is defined to be the limit as r→∞ of the difference of the sojourn times of a scattering state and of the associated free state in a ball of radius r, with the particle under the influence of a potential W(x). For W(x̲) ~ |x̲|−α (α>1) at infinity, we use a smooth localization function with the tail growing like r 1−α (δ>0, depending on W) instead of the characteristic function of a ball of radius r and it is shown that the time-delay exists and satisfies the Eisenbud-Wigner relation.

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