Generalized momentum equation of quantum mechanics

Like the Planck–Einstein relation E = ℏω, de Broglie’s \( {\mathbf{p}} = \hbar {\mathbf{k}} \) is another fundamental equation but the universal momentum formulation should be \( {\mathbf{p}} = \hbar {\varvec{\upbeta}} \). We propose the compelling evidence (vacuum Cherenkov radiation) and a new consequence which could lead to experimental checks is also worked out.