211Chapter 22Quantum Electrodynamics
The quantum mechanics developed by Schrödinger and Heisenberg did
not take into account the effects of Einstein’s theory of relativity. The
neglect of relativity did not limit the usefulness of the theory in any
serious way, however. The velocity of the electron in an atom or
molecule is never more that a few percent of the velocity of light and,
therefore, any relativistic corrections that are necessary are extremely
small. Non-relativistic quantum mechanics proved to be an extremely
useful tool in understanding the behaviour of atoms and molecules and
hence, in understanding the behaviour of macroscopic materials such as
solids, liquids and gases. In spite of its many practical applications
physicists were not completely satisfied with non-relativistic quantum
mechanics. First, there were some small details, which the theory did not
completely explain. But perhaps more importantly there were aesthetic
reasons for wanting to combine relativity and quantum mechanics.
Schrödinger, himself, as previously related had originally attempted to
incorporate relativity into his wave equations but failed because of the
complexity of the fully relativistic equations. Shortly after reporting his
non-relativistic results, Klein and Gordon resurrected Schrödinger’s
original relativistic equation. They were unable to do very much with it
except to write it down and point out the difficulties that attended its use.
Paul Dirac also attacked this problem and was able to develop a
different equation, which was fully relativistic and avoided some of the
difficulties of the Klein-Gordon equation. Dirac found an equation to
describe the electron, which combined the results of both quantum
mechanics and relativity. In addition, Dirac’s equation also explained the
spin of the electron and the presence of its magnetic properties.
Before Dirac’s theory, it was impossible to explain the magnitude of
the electron’s magnetic momentum in terms of its spin. Any mechanical