Functional approach to scattering in quantum mechanics

Sergio Giardino

Abstract We study the elastic scattering of quantum particles based on a real Hilbert space approach to quaternionic quantum mechanics ( QM) and derive expression for the wave function, the phase shifts, as well as the optical theorem for the case of a hard sphere scattering potential. The strong agreement between these new quaternionic results and the corresponding results in complex quantum mechanics reinforce the validity of the QM generalization of ordinary complex quantum mechanics ( QM).

W. W. Bell

A.S. Davydov

I. Richard Lapidus

Scattering lengths are obtained for the scattering of particles from two-dimensional circular barrier, hard circle, and delta function ring potentials using classical mechanics and quantum mechanics. These results will be of interest in a quantum mechanics course as a supplement to the discussion of three-dimensional scattering.

Izuru Fujiwara

Jianping Dong

The 2D space-fractional Schrödinger equation in the time-independent and time-dependent cases for the scattering problems in the fractional quantum mechanics is studied. We define the Green's functions for the two cases and give the mathematical expression of them in infinite series form and in terms of some special functions. The asymptotic formulas of the Green's functions are also given, and applied to get the approximate wave functions for the fractional quantum scattering problems. These results contain those in the standard (integer) quantum mechanics as special cases, and can be applied to study the complex quantum systems.