Quantum description of nuclear ensembles

Abstract

This chapter outlines the quantum ideas that underpin magnetic resonance and explains their link to classical physics. It discusses some of the essential concepts governing the quantum behaviour of ensembles of nuclear spins, including the nature of quantum states, the eigenvalue equation and observables, the measurement process, dynamics, and the Schroedinger equation. A detailed description of angular momentum is given along with discussion of the role of symmetry, rotation operators, and both product and total angular momentum representations. Statistical ensembles of spins are introduced and the density matrix and Liouville formalism outlined, along with the various tensor bases for the description of spin systems, both independent and coupled. The spin Hamiltonian is described in detail and the evolution of spin systems under various Hamiltonian terms is discussed using the density matrix description, along with suitable recession diagrams.