So far, only the physics of bosons has been discussed. However, by
far the most important particles in physics are electrons, and
electrons are fermions. The electronic structure of matter determines
almost all engineering physics: the strength of materials, all
chemistry, electrical conduction and much of heat conduction, power
systems, electronics, etcetera. It might seem that nuclear
engineering is an exception because it primarily deals with nuclei.
However, nuclei consist of protons and neutrons, and these are spin
Noninteracting electrons in a box form what is called a
free-electron gas. The valence electrons in a block of
metal are often modeled as such a free-electron gas. These electrons
can move relatively freely through the block. As long as they do not
try to get off the block, that is. Sure, a valence electron
experiences repulsions from the surrounding electrons, and attractions
from the nuclei. However, in the interior of the block these forces
come from all directions and so they tend to average away.
Of course, the electrons of a
free electron gas are
confined. Since the term “noninteracting-electron
gas” would be correct and understandable, there were few
possible names left. So
free-electron gas it was.
At absolute zero temperature, a system of fermions will be in the
ground state, just like a system of bosons. However, the ground state
of a macroscopic system of electrons, or any other type of fermions,
is dramatically different from that of a system of bosons. For a
system of bosons, in the ground state all bosons crowd together in the
single-particle state of lowest energy. That was illustrated in
figure 6.2. Not so for electrons. The Pauli exclusion
principle allows only two electrons to go into the lowest energy
state; one with spin up and the other with spin down. A system of
In the system ground state, the electrons crowd into the
The spectrum to the right in figure 6.11 shows the occupied energy levels in red. The width of the spectrum indicates the density of states, the number of single-particle states per unit energy range.
- Noninteracting electrons in a box are called a free-electron gas.
- In the ground state, the
2 spatial states of lowest energy are occupied by two electrons each. The remaining states are empty.
- The ground state applies at absolute zero temperature.