Nonrelativistic quantum mechanics, developed in the years from 1923 to 1926,
provides a unified and logically consistent picture of numerous phenomena in the
atomic and molecular domain. Following P.A.M. Dirac, we might be tempted
to assert: "The underlying physical laws necessary for the mathematical theory
of a large part of physics and the whole of chemistry are completely known."
provides a unified and logically consistent picture of numerous phenomena in the
atomic and molecular domain. Following P.A.M. Dirac, we might be tempted
to assert: "The underlying physical laws necessary for the mathematical theory
of a large part of physics and the whole of chemistry are completely known."
There are, however, basically two reasons for believing that the description
of physical phenomena based on nonrelativistic quantum mechanics is incomplete.
First, since nonrelativistic quantum mechanics is formulated in such a way as to
yield the nonrelativistic energy-momentum relation in the classical limit, it is
incapable of accounting for the fine structure of a hydrogen-like atom. (This
problem was treated earlier by A. Sommerfeld, who used a reiativistic
generalization of N. Bohr's atomic model.) In general, nonrelativistic quantum mechanics
makes no prediction about the dynamical behavior of particles moving at
reiativistic velocities. This defect was amended by the reiativistic theory of electrons
developed by Dirac in 1928, which will be discussed in Chapter 3. Second, and
what is more serious, nonrelativistic quantum mechanics is essentially a single-
particie theory in which the probability density for finding a given particle
integrated over all space is unity at all times. Thus it is not constructed to describe
phenomena such as nuclear beta decay in which an electron and an antineutrino
are created as the neutron becomes a proton or to describe even a simpler process
in which an excited atom returns to its ground state by "spontaneously" emitting
a single photon in the absence of any external field. Indeed, it is no accident that
many of the most creative theoretical physicists in the past forty years have spent
their main efforts on attempts to understand physical phenomena in which various
particles are created or annihilated. The major part of this book is devoted to the
progress physicists have made along these lines since the historic 1927 paper of
Dirac entitled "The Quantum Theory of the Emission and Absorption of
Radiation" opened up a new subject called the quantum theory of fields.
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