Maxwell Matter Waves

TL;DR

Maxwell matter waves propose a wave-based perspective of matter, introducing a matter vector potential and classical analogs to Maxwell's equations, leading to new optical-like systems and different interferometric behaviors.

Contribution

The paper introduces Maxwell matter waves as a novel wave description of matter, distinct from de Broglie waves, with a quantum mechanical foundation and classical electromagnetic analogs.

Findings

Maxwell matter waves are coherent excitations of a matter-wave field.

Their wavelength is linked to the drive frequency, not particle energy.

Interferometric measurements yield different results for Maxwell and de Broglie waves.

Abstract

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 $\omega_0$, 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 $\omega_0$ 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.