A free Gaussian wave packet solution of the Schrödinger equation can be converted to a wave packet rotating about the direction of motion. This Demonstration considers a three-dimensional Gaussian wave packet in the de Broglie–Bohm approach (often called Bohmian mechanics). In this theory, the particle has a well-defined trajectory in configuration space calculated from the total phase function. In practice, it is impossible to predict or control the quantum trajectories with complete precision. Real three-dimensional space is taken as the configuration space in this context.

In the de Broglie–Bohm approach, the possible orbits and velocities for this special wavefunction depend on the initial density and initial position of the starting particles in the three-dimensional configuration space. The particle rotates faster around the axis if the starting point is closer to the origin.

The graphics show the wave density (if enabled), the initial starting points of 32 possible orbits (shown as small yellow spheres), the actual positions (shown as small colored spheres) and 32 possible trajectories with the initial distance .