Dispersion

The image here shows three gaussian matter wave pulses all with different phase velocities (greater than , equal to, and less than the group velocity, respectively) but the same group velocity, the same initial position uncertainty/standard deviation, and the same dispersion coefficient. While starting out relatively well localized, the position of the particle repesented by these waves becomes increasingly uncertain. Regardless of the phase or group velocities, the matter wave is ultimately spread over an enormous region of space, the particle equally likely to be found just about anywhere in this broad region.