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

Quantum-mechanical description of Lense-Thirring effect for relativistic scalar particles