Two-Particle Schrödinger Equation Animations of Wavepacket--Wavepacket Scattering

Yannis Kominis, K. Hizanidis, Abhay K. Ram

P. R. Berman

Rubin H. Landau

Timothy Cox, John Lekner

Exact closed-form solutions of the time-dependent Schrödinger equation are obtained, describing the propagation of wavepackets in the neighbourhood of a potential. Examples given include zero reflection, total reflection and partial reflection of the wavepacket, for the , 1/ x 2 and δ( x ) potentials, respectively. In the first two of these cases the results are obtained using the methods of elementary supersymmetric quantum mechanics. This gives an introduction to supersymmetry in its simplest form, suitable for graduate or advanced undergraduate students. Animations of wavepacket propagation are provided.

Róbert E. Wyatt

Jon J. V. Maestri, Rubin H. Landau, Manuel José Páez

A simple and explicit technique for the numerical solution of the two-particle, time-dependent Schrödinger equation is assembled and tested. The technique can handle interparticle potentials that are arbitrary functions of the coordinates of each particle, arbitrary initial and boundary conditions, and multidimensional equations. Plots and animations are given here and on the World Wide Web of the scattering of two wave packet in one dimension.