hello! Does anybody know the physical justification of the de broglie relation p=\hbar k? or (i guess equivalently) for p=-i\hbar ∂/∂x ? i came across a more general "law" in laser physics, where momentum is seen as the gradient of the phase of a scalar light field (used in eg the paraxial wave equation). what is the exact connection between the phase (or actually it's gradient) and momentum, and where does it come from physically? thank you!