@fieldsolver: Here we use the Schrodingee equation to show the evolution of a single localized particle in within an infinite square well. The particle diffuses until it reaches the walls, where it reflects, giving rise to complex patterns know as quantum carpets. These patterns are periodic in space and time, such that the origin state is recovered at t=10/(4𝛑)~0.795, where the video ends. We add some extra time at the start and the end to appreciate this fact. While the solution is exact by using the sine base to represent the solution, the full series is truncated. As such, the solution is exact in time but truncated in space. Due to that, some numerical echoes remain due to the truncated nature of this exact result. The domain is a fixed square of side 1x1 with reflecting boundaries (infinite square well). We chose ħ/m=0.1 and dt=10/(2400𝛑)~1.33e-3 (exact in time). Colormap is scaled to be linear in sqrt(|Ψ|), to highlight small amplitude fluctuations. #physics #mathematics #differentialequations #visualization #calculus #numericalmethods #simulation #interference #waves #quantumphysics #well

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Sunday 03 May 2026 14:32:07 GMT