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PYThis simulation shows quantum interference of a wave packet hitting an S-shaped barrier with several slits.
In quantum mechanics, a particle (like an electron) is described by a wave function ( \psi(x,y,t) ).
The quantity ( |\psi|^2 ) represents the probability density, meaning where the particle is more likely to be found. At the beginning, we create a Gaussian wave packet on the left side, moving to the right with momentum ( k_0 ). When the wave reaches the curved barrier, most of it is blocked by the high potential ( V_0 ), but parts of the wave pass through the slits.
After passing through different slits, the waves spread and overlap.
Because quantum waves add together, they produce interference patterns: bright regions (constructive interference) and dark regions (destructive interference). The numerical method used is the split-step Fourier method. The Schrödinger equation has two parts: kinetic energy and potential energy.
We apply half of the potential evolution in real space, then transform the wave to Fourier space to apply the kinetic evolution, and finally apply the other half of the potential.
This works because in Fourier space, the kinetic operator becomes simple multiplication.
By repeating this process many times with small time steps ( dt ), we simulate the time evolution of the quantum system.
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