CHAPTER

2

THEORETICAL

DESCRIPTION OF NMR

SPECTROSCOPY

A rigorous treatment of the dynamics of nuclear spin systems and
NMR spectroscopy is afforded by the quantum mechanical representa-
tion known as thedensity matrix formalism(1, 2). Instead of following
only the evolution of the bulk magnetization vector as in the Bloch
model, the evolution of the density matrix provides a complete
description of the state of a spin system at any point during an NMR
experiment. The next few sections present a detailed overview of the
development of the density matrix theory and its application in the
simplest pulsed NMR experiments.

2.1 Postulates of Quantum Mechanics

A rather formal exposition of the mathematical concepts to be used
through the remainder of the text is presented first. Commonly, in
introductory quantum mechanics texts (3–5), quantum mechanical
orbital angular momentum is introduced via the classical concepts of
angular momentum. After establishing the relevant physics, the results
are generalized to include theintrinsicangular momentum of electrons
and nuclei. The intrinsic angular momentum does not have a classical
analog; accordingly, in this text, orbital angular momentum will not be

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