ROTATION OPERATOR APPROACH TO SPIN DYNAMICS AND THE EULER GEOMETRIC EQUATIONS

The rotation operator approach proposed previously is applied to spin dynamics in a time-varying magnetic field. The evolution of the wave f unction is described, and that of the density operator is also treated in terms of a spherical tenser operator base. It is shown that this f ormulation provides a straightforward calculation of accumulated phase s and probabilities of spin transitions and coherence evolutions. The technique focuses, not on the rotation matrix, but on the three Euler angles and its characteristic equations are equivalent to the Euler ge ometric equations long known to describe the motion of a rigid body. T he method usually depends on numerical calculations, but analytical so lutions exist in some situations. In this paper, as examples, a hyperb olic secant pulse is solved analytically, and a Gaussian-shaped pulse is calculated numerically.