Quantum Mechanics and Scattering

W. W. Bell

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).

S. Zienau

Jesús Pérez‐Ríos

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.

Jens Boos