Spin precession and energy conservation - art. no. 042101

In this paper, we examine the precession of a spin in a magnetic field, tre ating the particle and the applied magnetic field as a single closed system whose energy is conserved. Through two simple examples, it is shown that t he standard expression for spin precession emerges only indirectly; and as a first-order approximate result. For the first example, deviations from th e first-order result are easy to obtain, and are familiar from Stern-Gerlac h spin separation. For the second example, deviations from the first-order result are not practically possible to obtain. Beyond these two examples, i t is also shown within a semiclassical approach that the standard expressio n for spin precession in a magnetic field is always valid to first order, i rrespective of how the Hamiltonian depends on other dynamical variables of the system.