# Gaussian repulsive potential, large energy *w*(*r*) = exp(–0.04 *r*^{2})

### The potential (red line is the energy)

## Calculation of claassical trajectories

### Plot of trajectories on the potential surface

### Mapping (*y*, *t*) –> (*q*_{x}, *q*_{y})

### Zeroes of the Jacobian

Red curve shows the points where Jacobian of the transformation (*y*, *t*) –> (*q*_{x}, *q*_{y}) is zero.

Blue curve shows the points where Jacobian of the transformation (*y*, *t*) –> (*p*_{x}, *p*_{y}) is zero.
### Caustics

The same as above, but mapped into (*q*_{x}, *q*_{y}) 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.