Elementary applications of quantum-electrokinematics theorem

Summary

A preceding quantum-electrokinematics theorem obtained directly from the equations of Maxwell and of Schrödinger-Pauli, connects, by means of an arbitrary irrotational vector fieldF the wave function of a many-particle system, the internal scalar and vector potentials and the electric permittivity, with the current density and scalar potential, or voltage, on the surface of the system itself. In particular it shows the role of the current due to the particle spin. By means of proper choices ofF, it can be used to find old and new relations and results which, in general, would be harder to get by other methods. In the present work the theorem is used to compute a new expression of the output current of cylindrical two-terminal devices which, in its turn, is applied to a few elementary cases relevant to a single particle. They concern bounded systems, in stationary state, and the drift and spin currents, in non-stationary states, of a free electron and of an electron in a uniform and constant magnetic field. We obtain that a bounded electron cannot induce current at the output terminals and that, in more general terms, the results given by the new approach in the case of «small» sizes of the system, are very different from those obtained by means of the classical electrodynamics, whereas, as has to happen according to the classical limit principle, they tend to coincide for «great» sizes of the system itself. So, a not well-defined value of the spin component along the motion axis of a free electron generates a time-dependent fluctuation of the current proportional to its steady value. In the presence of a homogenous magnetic field, rather, the electron spin and its not well-defined value can generate steady and time-dependent contributions of the current, respectively. We also find that the spin acts on the current partition between two contiguous surfaces. The proposed applications, even they are elementary, can have interest because many phenomena in many-particle systems can be reduced to deal with the motion of a single particle.