Quantum degeneracy

Quantum degeneracy is a regime in which particles’ wavefunctions overlap significantly, making quantum statistics and collective quantum behavior important.

Thermal de Broglie wavelength: The characteristic wavelength associated with a particle’s thermal motion at a given temperature. Degeneracy becomes likely when this wavelength approaches the typical spacing between particles.
Bose–Einstein condensate: A state of matter in which a macroscopic number of bosons occupy the same quantum state. It is a prominent outcome of cooling a dilute bosonic gas into degeneracy.
Maxwell–Boltzmann statistics: Classical statistics describing distinguishable particles in the dilute, high-temperature limit. It approximates particle behavior when quantum-state overlap is negligible.
Wavefunction: A mathematical description of a quantum system that encodes probability amplitudes for measurement outcomes. Its spatial extent determines how readily neighboring particles’ states overlap.
Phase-space density: A measure of how densely particles occupy available position and momentum states. Its value indicates whether particles’ quantum states substantially overlap.
Degenerate Fermi gas: A fermion gas whose properties are governed mainly by Fermi–Dirac statistics rather than thermal motion. It is the characteristic low-temperature regime for fermionic matter.
Classical gas: A gas whose particles can be described without accounting for quantum statistics. Its dilute, warm regime lies opposite the quantum-degenerate limit.
Indistinguishable particles: Particles that cannot be distinguished by any intrinsic label or measurement. Indistinguishability makes quantum statistics relevant when states overlap.
Bose–Einstein statistics: Quantum statistics governing indistinguishable bosons, which can occupy the same quantum state. Bosonic degeneracy permits many particles to accumulate in one state.
White dwarf: A compact stellar remnant supported against gravity primarily by electron degeneracy pressure. Electron degeneracy lets a white dwarf resist collapse despite intense compression.

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