ABSTRACT

This chapter analyses the Bloch equations showing that quantum mechanics is not necessary in order to describe the Nuclear magnetic resonance (NMR) spectrum of a simple ensemble in which all of the spins are chemically equivalent with no J-coupling. It highlights that many phenomena, particularly multiple quantum coherence, defy description by classical analogy, and a quantum description is necessary. A general expression for a nuclear spin Hamiltonian for a single spin in an isotropic fluid (usually a liquid) must take into account two factors that together determine the energy of a particular state, chemical shift and J-coupling. The chapter illustrates the derivation that yields the energies of the stationary states of the system and the relative intensities of lines. It does not yield an expression for the line shape. In order to completely predict the appearance of the spectrum as was done in the classical case using the Bloch equations, the chapter considers time-dependent contributions to the Hamiltonian operator.