Gaussian repulsive 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

Gaussian repulsive potential Gaussian attractive potential near the barrier below the barrier modified Gaussian
modified Gaussian, larger energy inverted modified Gaussian, larger energy Gaussian repulsive potential, large energy Gaussian attractive potential, large energy Yukawa potential
Repulsive Yukawa potential Oscillating Gaussian potential Inverted oscillating Gaussian potential


Table of examples of two-dimensional potentials
Tulane Results of work at Tulane University with M. Herman
Waste icons More Unpublished reports

Designed by A. Sergeev.