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I've grown accustomed to mentally translating 'degenerate' to 'having equivalent energy', but the origin of the term always puzzled me, particularly in light of the more traditional English usage.

Etymology of the word suggests that it is formed from Latin prefix 'de-' and Latin root 'genus'. I suppose this is in line with the notion of equivalent energy: for example, because degenerate orbitals have the same energy, it might be impossible to tell their exact nature ("genus") via spectroscopy.

Is this conjecture correct? How does the term 'degenerate semiconductor' fit with it? (edit: I found a related question that says that degenerate electron gas

"is one where more than one electron (in fact two, one in each spin state) occupies each possible low-energy state up to the Fermi energy".

This sounds very similar to the Drude-Sommerfeld description of metals, so I am guessing that 'degenerate doping' refers to putting semiconductors into a regime where Drude-Sommerfield / degenerate electron gas gives an appropriate description of charge carriers)

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    $\begingroup$ This may get a better answer on History of Science and Mathematics. $\endgroup$ – knzhou Oct 13 '16 at 3:58
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    $\begingroup$ The term "degenerate" is also used to designate very highly doped semiconductors that become metal-like. For this also the term "degenerate doping" is used. $\endgroup$ – freecharly Oct 13 '16 at 6:02
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    $\begingroup$ Degenerate is commonly used to refer to limit special cases of something in mathematics. See also Wolfram MathWorld article about this word. $\endgroup$ – Ruslan Oct 13 '16 at 9:15
  • $\begingroup$ @freecharly - I am aware of that, hence the last sentence of my question. More precisely, I am wondering if "degenerate doping" in this case is still referring to equal energy levels? (I think I found the answer to this question, see edit) $\endgroup$ – Leo Alekseyev Oct 13 '16 at 9:43
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    $\begingroup$ I doubt this has anything to do with physics. A polynomial has degenerate roots if some roots coincide. Since eigenvalues have long been defined via roots of the characteristic polynomial (a term coined, I think, by Cauchy) the term carries over immediately. Also, perturbation theory works differently for the "degenerate" case hence people noticed. However, I cannot find good references. $\endgroup$ – Martin Oct 13 '16 at 10:37

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