Page 38 - PRINCIPLES OF QUANTUM MECHANICS as Applied to Chemistry and Chemical Physics

1.8 Physical interpretation of the wave function 29

x-directions. The passage of the atoms through the second magnet apparently
realigned their magnetic moments parallel and antiparallel to the positive y-
axis and thereby destroyed the previous information regarding their alignment
by the ®rst magnet.
The original Stern±Gerlach experiment has also been carried out with the
same results using sodium, potassium, copper, gold, thallium, and hydrogen
atoms in place of silver atoms. Each of these atoms, including silver, has a
single unpaired electron among the valence electrons surrounding its nucleus
and core electrons. In hydrogen, of course, there is only one electron about the
nucleus. The magnetic moment of such an atom is due to the intrinsic angular
momentum, called spin, of this odd electron. The quantization of the magnetic
moment by the inhomogeneous magnetic ®eld is then the quantization of this
electron spin angular momentum. The spin of the electron and of other
particles is discussed in Chapter 7.
Since the splitting of the atomic beam in the Stern±Gerlach experiment is
due to the spin of an unpaired electron, one might wonder why a beam of
electrons is not used directly rather than having the electrons attached to atoms.
In order for a particle to pass between the poles of a magnet and be de¯ected
by a distance proportional to the force acting on it, the trajectory of the particle
must be essentially a classical path. As discussed in Section 1.4, such a particle
is described by a wave packet and wave packets disperse with time±the lighter
the particle, the faster the dispersion and the greater the uncertainty in the
position of the particle. The application of Heisenberg's uncertainty principle
to an electron beam shows that, because of the small mass of the electron, it is
meaningless to assign a magnetic moment to a free electron. As a result, the
pattern on the detection plate from an electron beam would be suf®ciently
2
diffuse from interference effects that no conclusions could be drawn. How-
ever, when the electron is bound unpaired in an atom, then the atom, having a
suf®ciently larger mass, has a magnetic moment and an essentially classical
path through the Stern±Gerlach apparatus.

1.8 Physical interpretation of the wave function

Young's double-slit experiment and the Stern±Gerlach experiment, as de-
scribed in the two previous sections, lead to a physical interpretation of the
wave function associated with the motion of a particle. Basic to the concept of
the wave function is the postulate that the wave function contains all the

2 This point is discussed in more detail in N. F. Mott and H. S. W. Massey (1965) The Theory of Atomic
Collisions, 3rd edition, p. 215±16, (Oxford University Press, Oxford).