ABSTRACT
This chapter discusses the quasi-isotropic approximation (QIA) with the semiclassical asymptotics of the Pauli equations for spin 1/2 particles in a magnetic field. The case of spin 1/2 and the Pauli equation are taken to avoid complex manipulations and demonstrate the essence of novel features brought in by the QIA to this well-studied problem. The role of quantum constraints ensuring the description of the Stern-Gerlach splitting is played by the special initial conditions. The latter would imply that particle world lines are dependent on the states of particle spin. This is exactly what occurs in the Stern-Gerlach effect. However de Broglie was unable to find the expression for that additional term. Precession of the magnetic moment in this mode comes about due to interference mainly arising from the difference in eikonals corresponding to these modes. The solutions admit all the best known solutions as particular cases, in particular, the Stern-Gerlach particle trajectories and solutions of the Pauli-Galanin-Rubinow-Keller type.
