Dynamics of angular momentum coupling in an arbitrarily directed magnetic field

Abstract

The choice of an axis of quantization automatically selects those species from a bulk which could become stationary in a field-free environment with related spatial orientations of their coupling angular momenta. But if this axis fails to coincide with the direction of a uniform external magnetic field, a field-imposed transverse torque forces these atoms' total angular momenta into steady nutation that cannot be abolished by coupling-related internal torques. Making any stationary state impossible for these atoms, it also causes the contributions to the energy expectation value to oscillate. This is the result of a rigorous solution to the time-dependent Schrödinger equation describing the coupling dynamics of two spins 1/2 in an external field. Demanding to solve a four-dimensional system of coupled linear differential equations of first order, the bulkiness of even this simplest case already brings the calculations to the verge of becoming infeasible analytically.