Demos.DoubleWell.Main

WavePacket demo example: Double well potential

The double well potential is a prominent example where quantum mechanical tunneling plays a key role. In molecular physics symmetric double wells are frequently used to describe the "umbrella"-like motion of the ammonia (NH₃) molecule where the nitrogen atom tunnels through the plane spanned by the three hydrogen atoms.

Bound state calculations

Bound states well below the barrier separating the two (symmetric) wells occur as doublets with the energetic gaps being proportional to the tunneling rate. Bound states well above the barrier essentially behave like those of a single well potential. Wavefunctions localized around the barrier are found at intermediate energies. For illustration we use the (conditionally quasi-exactly solvable) Razavy double well potential for which a few analytical solutions are known, but only for specifc values of the parameters. Learn more ...

Gaussian wavepacket dynamics

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

Driven dynamics of open quantum system

We also consider the quantum dynamics of an (asymmetric) double well system driven by the interaction of its dipole moment with an external electric field (using semi-classic dipole approximation). Here we consider open system quantum dynamics thus allowing for dissipation and decoherence due to interaction with a thermal environment. In order to reduce the computation effort for solving the corresponding Liouville-von Neumann equation, we employ here the balanced truncation method for dimension reduction. Learn more ...