Quantum Statistical Distributions

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Each curve is computed directly from the real quantum-statistical occupation formula for the selected particle type, using a 3-D free-particle density of states g(E) ∝ √E. Drag μ toward the ground state (E=0) under Bose-Einstein statistics to approach the divergence that signals Bose-Einstein condensation; drag it deep under Fermi-Dirac statistics to build a sharp, sub-kT Fermi step. Total particle number N and average energy ⟨E⟩ are the numeric integrals ∫g(E)n(E)dE and ∫g(E)n(E)E dE / N over the plotted range, recomputed live.