Quantum concentration
The quantum concentration is the particle concentration of a system where the interparticle distance is equal to the thermal de Broglie wavelength.
Quantum effects become appreciable when the particle concentration is greater than or equal to the quantum concentration, which is defined as:
The quantum concentration for room temperature protons is about 1/cubic-Angstrom.
As the quantum concentration depends on temperature, high temperatures will put most systems in the classical limit unless they have a very high density e.g. a White dwarf.
For an ideal gas the Sackur–Tetrode equation can be written in terms of the quantum concentration as
