Gaussian attractive potential w(r) = –exp(–0.04 r2)
The potential (red line is the energy)
Calculation of claassical trajectories
Plot of trajectories on the potential surface
Mapping (y, t) –> (qx, qy)
Zeroes of the Jacobian
Red curve shows the points where Jacobian of the transformation (y, t) –> (qx, qy) is zero.
Blue curve shows the points where Jacobian of the transformation (y, t) –> (px, py) is zero.
Caustics
The same as above, but mapped into (qx, qy) plane. Primitive semiclassical approach
Absolute value of the wavefunction
Real part of the wavefunction
Real part of the wavefunction, including time dependence
More examples of potentials
Table of examples of two-dimensional potentials
Designed by A. Sergeev.