manipulating formulae, it is easy to check that the sum does work
out properly at the three sample points.Sets of compatible quantum numbers
Figure e shows some examples in which we can completely de-
scribe a wavefunction by giving a few numbers. These are referred to
as “quantum numbers.” It is important that the quantum numbers
we use in describing a state be compatible. By analogy, “Bond,
James, 007” would be a clear and consistent definition of the fa-
mous fictional spy, but in general this identification scheme would
not work, because although almost everyone has a first and last
name, most people do not have a license to kill with a correspond-
ing double-oh number.e/Three examples of sets of
compatible quantum numbers.
The laser beam in the figure is a state described according to
its definite valuespxandy, so we have the vanishing uncertainties
∆px= 0 and ∆y= 0. Since the Heisenberg uncertainty principle
doesn’t talk about anxmomentum in relation to ayposition, this
is OK. If we had been in doubt about whether this violated the
uncertainty principle, we would have been reassured by our ability
to draw the picture.
It is also possible to haveincompatiblequantum numbers. The
combination ofpxwithxwould be an incompatible set of quantum
numbers, because a state can’t have a definitepxand also a definite924 Chapter 13 Quantum Physics