Daily Archives: November 10, 2022

QM 101: Diffusion in 2D

Last time I began exploring the similarity between the Schrödinger equation and a classical heat diffusion equation. In both cases, valid solutions push the high curvature parts of their respective functions towards flatness. The effect is generally an averaging out in whatever space the function occupies.

Both equations involve partial derivatives, and I ignored that in our simple one-dimensional case. Regular derivatives were sufficient. But math in two dimensions, let alone in three, requires partial derivatives.

Which were yet another hill I faced trying to understand physics math. If they are as opaque to you as they were to me, read on…

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