Visualizing time-dependent wavefunctions

In my previous post, I presented a method of visualizing wavefunctions that are inherently complex-valued using a single plot that shows both the probability density and phase but frozen in time. Here, I complete this visualization by animating the plot.

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Visualizing 1D complex-valued wavefunctions

Visualizing wavefunctions is essential in quantum mechanics (or wave physics, in general).

For starters, let’s start with the eigenmode of the wave produced by the transverse displacement y of a string of length L (like that of a guitar) with fixed endpoints. The modes of these vibrations is given by y(x,t)=y_0 \sin(n \pi x/L)\cos(\omega_n t), where y_0 is the maximum displacement, x is the position, n is the mode number, and \omega_n is the mode frequency. Shown below is wavefunction for n=3 plotted as a single image for different snapshots in time.

String displacement for mode n=3. Source

Continue reading “Visualizing 1D complex-valued wavefunctions”