Semiclassical description of quantum rotator in terms of SU(2) coherent states

Abstract

We introduce coordinates of the rigid body (rotator) using mutual positions between body-fixed and space-fixed reference frames. Wave functions that depend on such coordinates can be treated as scalar functions of the group SU(2). Irreducible representations of the group SU(2) × SU(2) in the space of such functions describe their possible transformations under independent rotations of the both reference frames. We construct sets of the corresponding group SU(2) × SU(2) Perelomov coherent states (CS) with a fixed angular momentum j of the rotator as special orbits of the latter group. Minimization of different uncertainty relations is discussed. The classical limit corresponds to the limit j → ∞. Considering Hamiltonians of rotators with different characteristics, we study the time evolution of the constructed CS. In some cases, the CS time evolution is completely or partially reduced to their parameter time evolution. If these parameters are chosen as Euler angles, then they obey the Euler equations in the classical limit. Quantum corrections to the motion of the quantum rotator can be found from exact equations on the CS parameters.