Superposition state of the hydrogen

Two eigenstates of the hydrogen atom (quantum mechanical Coulomb problem) in a time-dependent superposition. States of the hydrogen are characterized by certain quantum numbers. Here the superposition contains states with different radial quantum numbers, hence the radial oscillation.

Note that the position probability density is a continuous distribution without sharp borders. The visualization shows two isosurfaces of the position probability density: The transparent isosurface belongs to a low value of the position probability density. The opaque isosurface belongs to a higher value. (Hence the probability to find the electron has a maximum inside the inner surface, and is very low outside the transparent surface). The colors of the isosurfaces symbolize the complex phase of the wave function in the usual way.

"Visual Quantum Mechanics - Book Two" investigates the behavior of solutions of the Coulomb problem in two and three dimensions. This movie was created with an application "QuantumGL" (an OpenGL based visualization tool distributed with Visual Quantum Mechanics Book Two).