Quantum scattering

Below, some simulations showing quantum scattering processes are presented.

The first one shows scattering in one dimension – an elementary question in quantum mechanics.

http://www.sgi.com/fun/java/john/wave-sim.html

The incoming particle is described by a wavepacket, with a Gaussian like envelope. The particle is scattered on a rectangular potential barrier or on a well (with an adjustable height).

See the simulation for different depths of the well and heights of the bareer. Track both the wave passing through bareer and the reflected.

Quantum mechanics shows, that even when the potential barrier is higher than the particle energy, the probability of the transmission through the barier is greater than zero. This makes a difference between a quantum particle and a tennis ball, which if flying too low (i.e. when its potential energy is too small) will not pass through the net.

Note that:

even in the case of the potential well there exists a reflected wave but (almost) does not exists a wave trapped inside the well, what would be expected in the case of a golf ball inside a hole
on the other hand, a trapped wave exists inside a potential bareer, but slowly "escapes" from it
in the case of a zero scattering potential, the wavepacket "dissappears" slowly – this is an effect resulting not only from Schrödinger's equation, but from a model of a particle, taken in a form of a "Gaussian" packet