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Chapter 3. Wave optics
Interference involves a single particle or photon propagating over
alternative paths, with an associated uncertainty in the path
taken. Position and momentum are described by a complex amplitude or wave function, with the amplitudes for alternative
paths adding to form a resultant complex amplitude. The absolute square of this amplitude gives the probability or intensity. We
will explore the wave function in detail in the following sections.
The spatial part of the wave equation governing the propagation
of this amplitude is the same for a free particle and a free photon.
Consequently, the formalism of scalar diffraction, interference, and
image formation for light can be directly applied to particles.
The path taken by a ray of light can be found from Fermat’s principle, which states that the physical path represents the shortest
possible transit time through a medium. The path taken by a particle can be found from the principle of least action, which states
that the physical path represents the minimum of the action integral. These two principles are strikingly similar. They arose from
a classical description, but as we shall see in the following, each
has a wave-optical analog as well. No classical analog exists for
the quantum mechanical description. However, quantum mechanical motion of particles and photons approaches classical behavior
in the high-energy limit. The analogy between particle optics and
light optics is deep and pervasive.
The central problem in this chapter is to solve for the wave function for a particle of charge q and rest mass m propagating in a
general electromagnetic potential. With this foundation, we then
explore a few of the important implications for wave optics. We
begin with a review of basic quantum mechanics governing particle motion. We confine the discussion to only those topics which
are relevant to the motion of a fast (unbound) charged particle
in a general electromagnetic potential. This is the subject of the
following section.
Chapter 3. Wave optics
Interference involves a single particle or photon propagating over
alternative paths, with an associated uncertainty in the path
taken. Position and momentum are described by a complex amplitude or wave function, with the amplitudes for alternative
paths adding to form a resultant complex amplitude. The absolute square of this amplitude gives the probability or intensity. We
will explore the wave function in detail in the following sections.
The spatial part of the wave equation governing the propagation
of this amplitude is the same for a free particle and a free photon.
Consequently, the formalism of scalar diffraction, interference, and
image formation for light can be directly applied to particles.
The path taken by a ray of light can be found from Fermat’s principle, which states that the physical path represents the shortest
possible transit time through a medium. The path taken by a particle can be found from the principle of least action, which states
that the physical path represents the minimum of the action integral. These two principles are strikingly similar. They arose from
a classical description, but as we shall see in the following, each
has a wave-optical analog as well. No classical analog exists for
the quantum mechanical description. However, quantum mechanical motion of particles and photons approaches classical behavior
in the high-energy limit. The analogy between particle optics and
light optics is deep and pervasive.
The central problem in this chapter is to solve for the wave function for a particle of charge q and rest mass m propagating in a
general electromagnetic potential. With this foundation, we then
explore a few of the important implications for wave optics. We
begin with a review of basic quantum mechanics governing particle motion. We confine the discussion to only those topics which
are relevant to the motion of a fast (unbound) charged particle
in a general electromagnetic potential. This is the subject of the
following section.