Recall that in the H-atom solution, we showed that the fact that the wavefunction
single-valued requires that the angular momentum quantum nbr be integer:
= 0, 1, 2.
However, operator algebra allowed solutions
= 0, 1/2,
Experiment shows that the electron possesses an intrinsic angular momentum called
By convention, we use the letter s instead of
for the spin angular
momentum quantum number : s = ½.
The existence of spin is not derivable from non-
It is not a form of orbital angular momentum; it cannot be derived from
(The electron is a point particle with radius r = 0.)
Electrons, protons, neutrons, and quarks all possess spin s = ½.
Electrons and quarks are
elementary point particles (as far as we can tell) and have no internal structure.
protons and neutrons are made of 3 quarks each.
The 3 half-spins of the quarks add to
produce a total spin of ½ for the composite particle (in a sense,
makes a single
Photons have spin 1, mesons have spin 0, the delta-particle has spin 3/2.
has spin 2.
(Gravitons have not been detected experimentally, so this last statement is a
Spin and Magnetic Moment
We can detect and measure spin experimentally because the spin of a
charged particle is always associated with a magnetic moment.
a magnetic moment is defined as a vector
associated with a loop of
The direction of
is perpendicular to the plane of the current loop
(right-hand-rule), and the magnitude is
between orbital angular momentum (not spin) and magnetic moment can
be seen in the following classical model: Consider a particle with mass
m, charge q in circular orbit of radius r, speed v, period T.