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

TL;DR

This paper establishes a correspondence principle linking quantum and classical equations for spin systems, enabling classical simulations to effectively study complex magnetic resonance phenomena.

Contribution

It formulates a correspondence principle for spin systems, validating classical equations as accurate representations of quantum dynamics in magnetic resonance problems.

Findings

Classical equations of motion match quantum equations for dipole-interacting spins.

Classical simulations successfully model free induction decay, spin echo, and Pake doublet.

The approach simplifies complex quantum magnetic resonance analyses.

Abstract

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.