Demos.FreeParticle.SchroediCat
The celebrated "Schrödinger Cat" state is a much discussed example for the apparent paradoxa of quantum mechanics. A simple yet elegant way to represent it in terms of wavefunctions in position space is a coherent superposition of two Gaussian wavepackets. Its characteristic properties are revealed in phase space (Wigner) representation
Two Gaussians displaced in position
The typical interpretation of "cat alive", "cat dead", and the non-classical "interference" state can be readily seen in Wigner representation, see the inspiring work by W. H. Zurek. In position representation the coherent nature is initially hidden. However, due to the effect of wavepacket dispersion, each of the corresponding position densities become wider as time goes by. Upon overlapping, the coherent nature of the superposition is reflected in the formation of oscillations in the position density.
| Matlab version | C++ version |
|---|---|
| Animation of evolving wavepacket | Animation of a coherent superposition and an incoherent sum of the two wavepackets. |
| Input data file | Input file and equivalent Python script |
| Logfile output | Logfile output |
Two Gaussians displaced in momentum
The opposite is true for two Gaussian packets shifted with respect to each other in the momentum direction. Initially, there are strong oscillations in the position density which get lost as the two wavepackets are moving in different directions. Nevertheless, the interference term is visible in the phase space representation all the time.
