Subatomic Physics

80 The Subatomic Zoo
cleus of the hydrogen atom, with a mass of about 2000me. The heaviest known
nucleus is about 260 times more massive than the proton. The masses (not counting
zero) consequently vary by a factor of over a billion. We shall return to the
masses a few more times, and details will become clearer as more specific examples
appear. However, just as it is impossible to understand chemistry without a
thorough knowledge of the periodic table, it is difficult to obtain a clear picture
of the subatomic world without an acquaintance with the main occupants of the
subatomic zoo.
A second property that is essential in classifying particles is the spin or intrinsic
angular momentum. Spin is a purely quantum mechanical property, and it is
not easy to grasp this concept at first. As an introduction we therefore begin to
discuss the orbital angular momentum which has a classical meaning. Classically,
the orbital angular momentum of a particle with momentum p is defined by
L = r × p, (5.2)
where r is the radius vector connecting the centerofmassoftheparticletothepoint
to which the angular momentum is referred. Classically, orbital angular momentum
can take any value. Quantum mechanically, the magnitude of L is restricted
to certain values. Moreover, the angular momentum vector can assume only certain
orientations with respect to a given direction. The fact that such a spatial
quantization exists appears to violate intuition. However, the existence of spatial
quantization is beautifully demonstrated in the Stern–Gerlach experiment, (1) and
it follows logically from the postulates of quantum mechanics. In quantum mechanics,
p is replaced by the operator −i�(∂/∂x,∂/∂y,∂/∂z) ≡−i�∇ and the orbital
angular momentum consequently also becomes an operator (2) whose z component,
for instance, is given by
�
Lz = −i� x ∂
�
∂
− y = −i�
∂y ∂x
∂
, (5.3)
∂ϕ
where ϕ is the azimuthal angle in polar coordinates. The wave function of a particle
with definite angular momentum can then be chosen to be an eigenfunction of L 2
and Lz: (3)
L 2 ψlm = l(l +1)� 2 ψlm
Lzψlm = m�ψlm.
(5.4)
1 Tipler and Llewellyn, Chapter 7; Feynman Lectures, II-35-3.
2 Tipler and Llewellyn, Chapter 7; Merzbacher, Chapter 9.
3 Some confusion can arise from the usual convention that classical quantities (e.g., L) andthe
corresponding quantum mechanical operators (e.g., L) are denoted by the same symbol. Moreover,
the quantum numbers are often also denoted by similar symbols (l or L). We follow this
convention because most books and papers use it. After some initial bewilderment, the meaning
of all symbols should become clear from the context. Occasionally we use the subscript op for
quantum mechanical operators.