Maxwell matter waves emerge from a perspective, complementary to de Broglie's, that matter is fundamentally a wave phenomenon whose particle aspects are revealed by quantum mechanics. Their quantum mechanical description is derived through the introduction of a matter vector potential, having frequency
ω0, to Schrodinger's equation for a massive particle. Maxwell matter waves are then seen to be coherent excitations of a single-mode of the matter-wave field. In the classical regime, their mechanics is captured by a matter analog of Maxwell's equations for the electromagnetic field. As such, Maxwell matter waves enable a spectrum of systems that have useful optical analogs, such as resonant matter-wave interferometric sensors and matter-wave parametric oscillators. These waves are associated with a wavelength that is tied to the drive frequency
ω0 rather than to the massive particle's energy, as is ordinarily the case with de Broglie matter waves. As a result, simple interferometric measurements lead to different outcomes for the two types of waves. While their apparent departure from de Broglie character is surprising, Maxwell matter waves are wholly consistent with quantum mechanics.
Phase-coherent matter-wave amplification was demonstrated using Bose- Einstein-condensed rubidium-87 atoms. A small seed matter wave was created with coherent optical Bragg diffraction. Amplification of this seed matter wave was achieved by using the initial condensate as a gain medium through the superradiance effect. The coherence properties of the amplified matter wave, studied with a matter-wave interferometer, were shown to be locked to those of the initial seed wave. The active matter-wave device demonstrated here has great potential in the fields of atom optics, atom lithography, and precision measurements.
The concept of matter wave radiation is put forward, and its equation is established for the first time. The formalism solution shows that the probability density is a function of displacement and time. A free particle and a two-level system are reinvestigated considering the effect of matter wave radiation. Three feasible experimental designs, especially a modified Stern-Gerlach setup, are proposed to verify the existence of matter wave radiation. Matter wave radiation effect in relativity has been formulated in only a raw formulae, which offers another explanation of Lamb shift. A possible mechanics of matter teleportation is predicted due to the effect of matter wave radiation.