At this stage, it becomes necessary to look somewhat closer at the
various particles involved in quantum mechanics themselves. The
analysis so far already used the fact that particles have a property
called mass, a quantity that special relativity has identified as
being an internal amount of energy. It turns out that in addition
particles have a fixed amount of build-in
angular
momentum, called spin.
Spin reflects itself, for
example, in how a charged particle such as an electron interacts with
a magnetic field.
To keep it apart from spin, from now on the angular momentum of a
particle due to its motion will on be referred to as
orbital
angular momentum. As was discussed in chapter
4.2, the square orbital angular momentum of a particle is
given by
The square spin angular momentum of a particle is given by a similar
expression:
(5.14) |
Particles with half integer spin are called “fermions.” For example, electrons, protons, and neutrons all
three have spin
Particles with integer spin are called “bosons.” For example, photons have spin
The spin angular momentum in an arbitrarily chosen
(5.15) |
The common particles, (electrons, protons, neutrons), can only have
spin angular momentum
It may be noted that the proton and neutron are not elementary
particles, but are baryons, consisting of three quarks. Similarly,
mesons consist of a quark and an anti-quark. Quarks have spin
Spin states are commonly shown in “ket notation” as
Key Points
- Most particles have internal angular momentum called spin.
- The square spin angular momentum and its quantum number
are always the same for a given particle.
- Electrons, protons and neutrons all have spin
. Their spin angular momentum in a given direction is eitheror .
- Photons have spin one. Possible values for their angular momentum in a given direction are
, zero, or, though zero does not occur in the direction of propagation.
- Particles with integer spin, like photons, are called bosons. Particles with half-integer spin, like electrons, protons, and neutrons, are called fermions.
- The spin-up state of a spin one-half particle like an electron is usually indicated by
or . Similarly, the spin-down state is indicated byor .
Delta particles have spin
Delta particles have spin