Schrödinger Equation (2D)

This 2D companion solves the same 1D time-dependent Schrödinger equation as the 3D version — a Gaussian wave packet advanced by an explicit finite-difference (FTCS) update of its real and imaginary parts — but reads it as a plain instrument panel rather than a WebGL scene. The top pane plots the potential and the wavefunction in whichever representation you pick (probability density |ψ|², or the raw real/imaginary parts), with phase-coloured bars showing the local complex phase under the curve. Below it, a scrolling space-time strip stacks every frame's |ψ|² as a new column of a heatmap, so reflection off a well, spreading through a harmonic trap, or the faint transmitted tail that leaks through a barrier become visible streaks you can trace with your eye instead of a moving dot you have to remember. A live readout tracks the norm (should hold near 1), the mean position ⟨x⟩, the mean momentum ⟨p⟩ computed from the wavefunction's phase gradient, the fraction of probability that has crossed to the right half of the grid, and a numerical estimate of the total energy — quantities a WebGL shader plot shows but does not print as numbers.