Spin 1 and 3/2 systems in quadrupole fields

Abstract

We study the Unitary evolution of spin 1 and 3/2 systems in an arbitrary external quadrupole field. Explicit solutions in closed form are obtained. These are employed to examine the notion of ‘ precession ’ of the vector polarization P = ⟨J⟩ in the field. Finally, in view of the large number of invariants that we find, we develop a method based on the lagrangian formulation using which, and without having to solve the equations of motion, the invariants can be discovered when a (quantum) statistical assembly evolves in an external field.