File:QuantumOccupancies.png
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English: Quantum occupancy nomograms, where for example when (ε-μ) = kT we find that fFD = 1/(e+1) ≈ 0.269, fMB = 1/e ≈ 0.368, and fBE = 1/(e-1) ≈ 0.582 so that for a given value of (ε-μ)/kT, as expected, fFD ≤ fMB ≤ fBE.
At top: The dashed lines denote filling fractions for Fermi-Dirac (FD) states whose energy ε is offset by integer-multiples of kT from the Fermi chemical-potential μ. In the FD case, the average number of particles per state and the fraction of states occupied are one and the same. At bottom: The "low-density" Maxwell-Boltzmann (MB) approximation is a dashed grey curve which neglects chemical potential μ altogether, and it is also the fraction of Bose-Einstein (BE) states occupied. From bottom up the dotted curves denote contributions to the BE particle-average from those occupied energy-levels which have a population of one, two, three and four particles (or excitations), respectively. |
| Date | |
| Source | Own work |
| Author | P. Fraundorf |
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| current | 14:38, 12 November 2013 | | 431 × 599 (22 KB) | Unitsphere (talk | contribs) | User created page with UploadWizard |
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