The ground state for a system of noninteracting spinless bosons is
simple. The ground state is defined as the state of lowest energy, so
every boson has to be in the single-particle state
If the bosons have spin, this is additionally multiplied by an
arbitrary combination of spin states. That does not change the system
energy. The system energy either way is
Graphically, the single-particle ground state
Physicists like to talk about “occupation numbers.” The occupation number of a single-particle
state is simply the number of particles in that state. In particular,
for the ground state of the system of noninteracting spinless bosons
above, the single-particle state
Note that for a macroscopic system,
Key Points
- For a system of bosons in the ground state, every boson is in the single particle state of lowest energy.