The Stokes Parameters in the Group-Theoretic Scheme of Quantum Mechanics

Abstract

The hidden parameters problem in quantum mechanics is considered here on the base of grouptheoretic approach which includes the complete set of observables indispensably. The last ones are the bilinear Hermitian forms constructed from the Schroedinger equation solutions and its ?rst derivatives, they satisfy the algebraic completeness condition and coincide with the well known Stokes parameters. These Hermitian forms, obtained for the simplest standard problem of particle transmission above potential step, had been compared with the Hermitian forms which are usually considered in this problem, and an additional ones, which may be obtained within the framework of an ordinary schemes of quantum mechanics. It is shown that the generally recognized schemes of the problem solution lead to violation of some conservation laws on the step directly. On the contrary, the group-theoretic approach leads to ful?llment of all necessary conservation laws everywhere at the same time. It is also shown that the complete set of observables leads a probabilistic interpretation in quantum mechanics to be excessive.