The quantum mechanics correspondence principle for spin systems and its application for some magnetic resonance problems

Problems of interacting quantum magnetic moments become exponentially complex with increasing number of particles. As a result, classical equations are often used but the validity of reduction of a quantum problem to a classical problem should be justified. In this paper we formulate the correspondence principle, which shows that the classical equations of motion for a system of dipole interacting spins have identical form with the quantum equations. The classical simulations based on the correspondence principle for spin systems provide a practical tool to study different macroscopic spin physics phenomena. Three classical magnetic resonance problems in solids are considered as examples - free induction decay (FID), spin echo and the Pake doublet.

💡 Research Summary

The paper addresses the long‑standing difficulty of modeling interacting quantum magnetic moments, whose Hilbert space grows exponentially with the number of spins. Because of this, researchers often resort to classical equations of motion, but the legitimacy of such a reduction has rarely been demonstrated rigorously. The authors formulate a “correspondence principle” that shows the equations of motion for a system of dipole‑coupled spins have exactly the same formal structure in both quantum mechanics and classical mechanics. Starting from the full quantum Hamiltonian that includes Zeeman interaction with an external magnetic field and the magnetic‑dipole interaction between every pair of spins, they apply the Heisenberg equation of motion. Using the canonical commutation relations (