Quantum harmonic oscillator is one of the few quantum mechanical systems for which an exact, analytic solution is known. It is especially useful because arbitrary potential can be approximated by a harmonic potential in the vicinity of the equilibrium point.
The wave-like behavior of a particle confined to a harmonic well is described by the wave functions of the quantum harmonic oscillator. These are the solutions to the corresponding quantum mechanical Schroedinger equation and they determine the probability to find the particle in a particular space region.
This app visualizes the eigenstates of the three-dimensional quantum harmonic oscillator by drawing the cross-section surfaces of the square of the wave function in OpenGL, using the Marching Cubes algorithm. The spherical coordinate basis is employed.
- Select the eigenstate by specifying the quantum numbers k, l and m, or pick a random one.
- Change the discretization step size.
- Choose the total probability to find the particle inside the drawn orbital surface.
- Zoom and rotate the surface with your fingers.