  Exact expression for the Foldy-Wouthuysen Hamiltonian of scalar particles is
used for a quantum-mechanical description of the relativistic Lense-Thirring
effect. The exact evolution of the angular momentum operator in the Kerr field
approximated by a spatially isotropic metric is found. The quantum-mechanical
description of the full Lense-Thirring effect based on the Laplace-Runge-Lenz
vector is given in the nonrelativistic and weak-field approximation.
Relativistic quantum-mechanical equations for the velocity and acceleration
operators are obtained. The equation for the acceleration defines the
Coriolis-like and centrifugal-like accelerations and presents the
quantum-mechanical description of the frame-dragging effect.
