Two-Particle Schroedinger Equation Animations of Wavepacket-Wavepacket Scattering; Research, Education, or Computing?

Rubin H. Landau

P. R. Berman

Babur M. Mirza

We investigate wavepacket solutions for time-dependent Schoedinger equation in the presence of an exponentially decaying potential. Assuming for travelling wave solutions the phase to be a linear combination of the space and time coordinates, we obtain two distinct wavepacket solutions for the Schroedinger equation. The wavepackets counterpropagate in space at a constant velocity without any distortion or spreading thus retain their initial form at arbitrarily large distances.

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.

V. Milos, V. Kundrát, Jiri Prochazk