Preface
xi
with respect to the special theory of relativity. Interestingly, this
adds no significant complexity over the historical non-relativistic
treatments, but does lead to a more accurate mathematical description. We therefore keep everything relativistically correct to
the extent possible.
Chapter 3 describes wave optics. We begin with a review of quantum mechanics, limited to only those ideas that impact the motion
of a single charged particle. We begin with the non-relativistic approximation and Schr¨ odinger’s equation. Relativity is introduced
later in the form of the Klein–Gordon equation. This skirts a
rigorous treatment of spin, but keeps things from becoming too
abstract, while producing a practical result. The discussion culminates with the quantum mechanical solution for the propagation of
the single-particle wave function in a general electromagnetic potential. The correspondence between wave optics and geometrical
optics in the classical limit emerges naturally from this discussion.
We then discuss diffraction and interference, starting with Huygens’ principle, and proceeding through the scalar Helmholtz equation, the Huygens–Fresnel relation, the Fresnel approximation, and
the Fraunhofer approximation. Next we discuss a number of useful
examples, including formation of an image and a diffraction pattern, the general optical transformation from object to image, and
the fundamental relationship between diffraction and Heisenberg’s
uncertainty principle.
Chapter 4 describes the two-body scattering problem, which is basic to the interaction of a fast charged particle with matter. Most
of the relevant information about the scattering process is contained in the scattering cross section, which is derived first in the
classical approximation, and then in the quantum mechanically.
Chapter 5 describes electron emission as a practical consequence
of quantum mechanics. Finally, the appendices contain two essential mathematical topics, which are repeatedly referred to in the
main text.
xi
with respect to the special theory of relativity. Interestingly, this
adds no significant complexity over the historical non-relativistic
treatments, but does lead to a more accurate mathematical description. We therefore keep everything relativistically correct to
the extent possible.
Chapter 3 describes wave optics. We begin with a review of quantum mechanics, limited to only those ideas that impact the motion
of a single charged particle. We begin with the non-relativistic approximation and Schr¨ odinger’s equation. Relativity is introduced
later in the form of the Klein–Gordon equation. This skirts a
rigorous treatment of spin, but keeps things from becoming too
abstract, while producing a practical result. The discussion culminates with the quantum mechanical solution for the propagation of
the single-particle wave function in a general electromagnetic potential. The correspondence between wave optics and geometrical
optics in the classical limit emerges naturally from this discussion.
We then discuss diffraction and interference, starting with Huygens’ principle, and proceeding through the scalar Helmholtz equation, the Huygens–Fresnel relation, the Fresnel approximation, and
the Fraunhofer approximation. Next we discuss a number of useful
examples, including formation of an image and a diffraction pattern, the general optical transformation from object to image, and
the fundamental relationship between diffraction and Heisenberg’s
uncertainty principle.
Chapter 4 describes the two-body scattering problem, which is basic to the interaction of a fast charged particle with matter. Most
of the relevant information about the scattering process is contained in the scattering cross section, which is derived first in the
classical approximation, and then in the quantum mechanically.
Chapter 5 describes electron emission as a practical consequence
of quantum mechanics. Finally, the appendices contain two essential mathematical topics, which are repeatedly referred to in the
main text.