Animation of a Rotating Electron Wave Function

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Animation of a Rotating Electron Wave Function

The Rotation Axis of Spherical Harmonics in Atomic Orbitals

In Bohr's model of the atom, electrons are pictured as moving around the nucleus in fixed orbits. In modern quantum-mechanical descriptions of atomic orbitals, such as the visualization below, electrons are not depicted as particles traveling along definite paths.

In the second row, the image suggests a relationship between the red sphere and the orbital's angular momentum, but it does not make the axis of rotation clear.

By contrast, the "Wave Functions Illustrated by Phase" page of the Mathematical Science Art Museum visualizes wave functions in the following way:

1. Brightness represents amplitude.
2. Hue represents phase.

This approach makes it possible to animate the apparent motion of electrons around the nucleus.

I therefore experimented with creating these visualizations in JavaScript.

Animation of Electron Rotation

A GIF animation of the rotating electron wave function for the 4f orbital of the hydrogen atom is available here:

GIF animation of the rotating electron wave function

The animation can also be viewed on YouTube.

The video was produced using the following steps:

1. Use a Monte Carlo method to distribute points according to the probability density.
2. Color each point according to its phase.
3. Animate the wave function by varying each point's phase over time.

Changing only the phase makes the wave function appear to rotate.

You can also try a JavaScript-based animation of the electron wave function in a hydrogen atom here:

JavaScript animation of the electron wave function

Orbital State

The default state is (n, l, m) = (4, 3, 1). Here, n is the principal quantum number, l is the azimuthal quantum number, and m is the magnetic quantum number.

Click the "State" button to choose from states such as (1, 0, 0), (2, 1, 1), (3, 2, 1), and (3, 2, 2). In the (1, 0, 0) state, no rotation occurs; only the global phase changes.

Number of Points

The default number of points is 51,200. If your computer cannot run the animation smoothly, click the "Number" button to reduce the number of points.

• Bell's Inequality Explained with Venn Diagrams (2018/9/2)
• Spin in Quantum Mechanics: Is It Really a Rotation? (2014/9/1)
• The Many-Worlds Interpretation of Quantum Mechanics (2013/6/22)

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