Wavepacket Demo
A Gaussian wavepacket travels toward a potential. Part of it reflects and part tunnels through, even when its mean energy is below the barrier.
Potential
Wavepacket
Reflected0%
Transmitted0%
Mean energy0
Time0
What it models
A single non-relativistic particle in one dimension, iψt = −½ψxx + V(x)ψ with ħ = m = 1. Transmission below the barrier height is quantum tunnelling; the double barrier shows resonances where transmission jumps at particular energies.
Method
- Strang split-step Fourier on 2,048 points with a radix-2 FFT written for this page; second order in time and unitary apart from the absorbing edges.
- Absorbed probability is credited to the side it left from, so reflected plus transmitted stays at 100%.
- Δt = 0.02, six steps per frame.