Probability amplitude description of the dynamics of charged particles in a magnetic field in the macrodomain

The set of Schrödinger-like equations obtained earlier by the author [Phys. Rev. Lett. 26, 417 (1971), Phys. Rev. A 31, 3951 (1985)] for the charged particle dynamics in an inhomogeneous magnetic field in the macrodomain, are derived here starting from the quantum-mechanic Schrödinger equation in its path-integral representation. This derivation enables a generalization of the equations to include a curl-free vector potential in the Schrödinger-like equations. In view of the amplitude character of the latter equations, which now descends directly from that of the quantum-mechanic Schrödinger equation, they now predict the existence in the macrodomain of all such phenomena, which are characteristic of a probability amplitude theory, e.g., the interference, and the observation of a curl-free vector à la Aharonov-Bohm. A discrete energy structure, predicted as interference maxima and minima has already been observed by the author with his co-workers [Mod. Phys. Lett. A 8, 167 (1993)]. A prediction is now made for the observability of a curl-free vector potential in the macrodomain, in the context of the present problem.