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Can someone explain what is the meaning of single particle states? I found this on Huang's book on statistical mechanics while writing distribution functions (e.g, Bose-Einstein or Fermi-Dirac). We were dealing with states of the full system in the partition function and suddenly why did we need single particle states? I cannot understand. Please help.

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2 Answers 2

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A single-particle state is the eigenstate of a single-particle hamiltonian, i.e., a hamiltonian describing a single particle, usually without interactions with other particles.

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  • $\begingroup$ Why do single-particle states appear in distribution functions? The partition function contains energy levels of the full system. $\endgroup$ Commented Mar 12, 2019 at 8:05
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    $\begingroup$ If you talk about distribution functions, like the Fermi-Dirac distribution, or the Bose-Einstein distribution function, the reason is that they describe non-interacting systems, where the total system energy is simply the sum of single-particle energies of occupied states. $\endgroup$
    – flaudemus
    Commented Mar 12, 2019 at 15:58
  • $\begingroup$ @ flaudemus, "describe non-interacting systems..." System or subsystems? Maybe more clear be: Describe systems that can be represented as a set of non-interacting subsystems, and then the partition function of a system is the product of the partition functions of subsystems? $\endgroup$ Commented Mar 12, 2019 at 18:21
  • $\begingroup$ @AlekseyDruggist: to be more precise: systems of non-interacting fermions or bosons. $\endgroup$
    – flaudemus
    Commented Mar 12, 2019 at 21:09
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A single particle state is defined as that which belongs to a vector space associated with an irreducible representation of the Poincare algebra and other internal symmetries. Please refer to The Quantum Theory of Fields, Volume 1, Chapter 2 by Steven Weinberg.

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  • $\begingroup$ Maybe you can clarify how and why the QFT definition applies in this case. $\endgroup$ Commented Mar 11, 2019 at 10:12
  • $\begingroup$ The question doesn't give enough information on what is the calculation being referred to. Weinberg's definition gives a good notion of how to interpret bound states as single particle states which seemed relevant to me here. I don't think this definition is restricted to QFT or should be termed "QFT definition". It is the clearest definition I know of single particle states. The other upvoted answer here is in fact circular. $\endgroup$ Commented Mar 12, 2019 at 14:24

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