The Generalized Spin Precession Equation

Abstract

We had shown that every two-level system can be mapped onto an effective spin-$\frac {1}{2}$ system, and its Hamiltonian onto an effective magnetic interaction. Furthermore, we had learned that there is a one-to-one correspondence between the precession equation for the quantum mechanical expectation values of the spin components and the classical equations of motion of the spinning top. These ideas are extended to arbitrary quantum numbers of the particles and their multipole interactions. We shall arrive at a generalized precession equation, but beyond spin-$\frac {1}{2}$ the correspondence to classical mechanics is lost. A special bra-ket notation for tensor operators is introduced that makes calculations simpler than is found in textbooks on quantum mechanics.