Summary

Abstract

We have considered a variety of effects—line widths, chemical shifts, Knight shifts, hyperfine splittings—a bewildering array of seemingly special cases. As we look back, we see some effects that occur in first-order perturbation theory, others that require a higher order. Since we have discussed the phenomena one by one, it is appropriate to summarize by writing a single Hamiltonian that includes everything. As we contemplate it, we should remind ourselves of the significance of each term. We write below the Hamiltonian describing a nucleus interacting with an electron in the presence of a magnetic field H ₀. We define the vector potentials A ₀, associated with the field H ₀, and A _n , associated with the field at the electron owing to the nuclear moment (An = µ × r/r ³ normally). We also define the quantity

$$\pi = \frac{\hbar}{i}\nabla + \frac{e}{c}\mathop A\nolimits_0 $$

((11.1))

.