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In this work, a precise quantum analog of spin precession of classical theory is obtained. As an example, a neutral Dirac particle (neutron) is considered. A non-stationary wave function is a superposition of wave functions with counter spins. It is used to calculate the average value of the spin operator. It is demonstrated that classical and quantum theories lead to an adequate description of the spin precession.

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At present a number of methods of constructing the Poincare-invariant spin operators for relativistic particles with half-integer spin in the one-particle theory are well known. The method of odd operator constructing, the Lorentz method of bilinear covariant form transformation, and the method with the Foldy-Wouthuysen representation belong to them. New approaches to the construction of spin operators are developed in the present work, namely, a method of separating space-like component directly from the spin matrices of bilinear covariant forms, including the method of multiplication of the covariant Hamiltonian of the Dirac equation by these matrices. By this means we succeeded in constructing the Poincare-invariant spin operators by simpler and mathematically faultless methods.