Demos.DoubleWell.Gaussian1D

If a Gaussian wavepacket localized near one of the (symmetric) potential wells is chosen as an initial wavepacket, the wavefunction dynamics depends strongly on its initial momentum. At high energies the barrier can be overcome in a classical-like manner. At low energies, the wavepacket can tunnel through the barrier

Low energy:
Below the barrier

At lowest energies (here not much higher than ground state energy which is close to − 9), the wavepacket can in principle tunnel through the barrier. In practice, we don't see that here, because of too long tunneling times.

• Animated wavefunctions
• Input data file
• Logfile output

Medium energy:
Just at the barrier

Choosing the momentum such that the initial energy is close to the barrier height which is here at −0.69 we see substantial barrier crossing.

• Animated wavefunctions
• Input data file
• Logfile output

High energy:
Passing over barrier

At much higher energy, the density fills up rather quickly all of available phase space volume.

• Animated wavefunctions
• Input data file
• Logfile output