De Broglie Phase Wave Animation覧覧覧覧覧
The animation above illustrates schematically the relationship between the motion of a particle and the associated de Broglie phase wave.
The particle, which is moving to the right, is represented by the red circle. The "internal periodic phenomenon" assumed by de Broglie is represented schematically by the up-and-down motion of the particle. Note that this is for the purpose of illustrating the instantaneous phase of the internal periodic phenomenon only; it is not intended to convey that the particle is literally moving up-and-down. Rather, the motion of the particle is smoothly to the right as illustrated by the steady rightward motion of the vertical line attached between the "particle" and the horizontal axis.
The de Broglie phase wave is represented by the green sine wave, which also propagates to the right. Note that the speed of the phase wave (phase velocity) exceeds that of the particle (group velocity). In the actual phase waves of de Broglie, the product of the phase velocity and the group velocity is cｲ. For massive particles, the group velocity is always less than c, and the phase velocity is always greater than c. For massless particles (photons, for example) the group and phase velocities both equal c.
Note that, in accordance with the de Broglie theory, the phase of the phase wave at the position of the particle always exactly matches the instantaneous phase of the internal periodic phenomenon associated with the particle, though (except for massless particles) the particle and the phase wave move, or propagate, with different velocities. The constant match between the phase of the phase wave and the phase of the internal periodic phenomenon at the position of the particle is illustrated above by the invariable coincidence of the red circle and the green sine wave. For example, when the phase wave reaches its peak value at the position of the particle, the internal phenomenon also reaches its peak value. Likewise for all other phase values.
Finally, the tracking of the red circle on the green sine wave is intended only to render the perfect coincidence of the wave and particle phases at the position of the particle more obvious. Otherwise, no meaning is to be attached to the amplitude of the internal periodic phenomenon being equal to the amplitude of the phase wave.