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”

Itch to blog

My side trips with physics outside of my PhD work.

Visualizing real and abstract concepts is essential in learning physics, especially for visual learners like myself. If I am unable to paint a picture of the physics in my head, I basically don’t understand it.

When I learned Python for computations, I immediately fell in love with it. It is easy to learn and use, and it offers a versatile and powerful set of visualization tools. Even if I am using MATLAB for my current PhD work (I’m an experimental physicist), I still find time playing with Python. This blog will be my way of sharing tiny bits of this adventure.

This is my first blog and I hope I can manage and update it when needed.

The image above was taken during my adventures (cycling) in the real world. Spot the the kangaroos!