Quantum concentration

The quantum concentration n_Q is the particle concentration (i.e. the number of particles per unit volume) of a system where the interparticle distance is equal to the thermal de Broglie wavelength or equivalently when the wavefunctions of the particles are touching but not overlapping.

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Quantum effects become appreciable when the particle concentration is greater than or equal to the quantum concentration, which is defined as:

where:

M is the mass of the particles in the system

k is the Boltzmann constant

T is the temperature as measured in kelvin

is the reduced Planck constant

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.