Quantum wave packet (2D)

This demonstration shows the numerical solution of the time-dependent, two-dimensional Schroedinger equation in the presence of an obstacle.

The initial state is a Gaussian wavepacket with adjustable kinetic energy. The obstacle consists of either a cylindrical barrier, or well, with adjustable height and width, or a pair of slits with adjustable width and spacing. If a cylindrical obstacle is chosen, it is shown in red if it is a barrier and in yellow if it is a well.The boundaries are periodic (so the solution is useless once the wavepacket reaches the boundary).

Available user controls are the start/stop and restart buttons, sliders for setting the relative height of the displayed wave packet (the actual solution is of course normalized), the kinetic energy, the details of the obstacle (cylinder height and radius, or slit width and spacing), the number of integration steps between updates and the lattice size (larger is better but takes longer to compute), and a choice of obstacle types. Drag with the mouse to change the view direction and elevation.

Note: this demonstration requires Java3D.

(c)   D. Rapaport