According to Dirac and Schrödinger theory, states with the same
*n* and *j* quantum numbers but different *l* quantum numbers ought to
be degenerate. However, a famous experiment by Lamb and Retherford in
1947 showed that the and
states of the hydrogen
atom were not degenerate, but that the *s* state had slightly higher
energy by an amount now known to be .
The effect is explained by the theory of quantum
electrodynamics, in which the electromagnetic interaction itself
is quantized. Some of the effects of this theory which cause the Lamb
shift are shown in the Feynman diagrams of figure 5.

**Figure 5:** Feynman loop diagrams showing some effects that contribute to the
Lamb shift.

Table 3 shows how much each of these contribute to the splitting of and .

**Table 3:** Contribution of different effects to the energy splitting of
and in hydrogen. Numbers are given in units of frequency
.

The most important effect is illustrated by the center diagram, which
is a result of the fact that the ground state of the electromagnetic
field is not zero, but rather the field undergoes ``vacuum fluctuations''
that interact with the electron. Any discussion of the calculation is
beyond the scope of this paper, so the answers will merely be given.
For *l*=0,

where *k*(*n*,0) is a numerical factor which varies slightly with *n* from
12.7 to 13.2. For ,

for , where *k*(*n*,*l*) is a small numerical factor <0.05
which varies slightly with *n* and *l*. Notice that the Lamb shift is
very small except for *l*=0.

Mon Oct 26 15:21:07 EST 1998