Wave packet with special relativity demonstrating quantum rules, Schrodinger´s equation and propagator integral

The physics of special relativity is applied to a wave-packet model of a particle without the usual de Broglie-like assumption of Planck´s rule, E=hv. The velocity of the particle is equated to the group-velocity of the wave-packet to associate the particle with its wave-packet. With such an identification it is demonstrated using special relativity that the momentum four-vector, P=(p, E/c²), of the particle is parallel and proportional to a central wave-number four-vector, K₀=(k₀, omega ₀/c²), of the particle´s wave-packet. The constant of proportionality, relating these two four-vectors, has the dimension of action and by diffraction experiments it has the value h/2 pi where h is Planck´s constant. This refinement of the de Broglie wavelike nature of a particle suggests that special relativity underlies quantum physics more deeply than heretofore believed. The above quantum rules are used to find the wave-packet function in the one-dimensional case of a non-relativistic free particle and a particle in a conservative force field of potential V(x).