I am beginning with second quantification language so i saw that if we are in grand canonical ensemble then:
$$ H=H_0 - \mu N $$

naturally i thought that this $ \mu $ would be included in the weight factor of the statistical average but i am surprised too find it in H, is it equivalent or is does this have a physical sens that i am not seeing ?

  • $\begingroup$ hint: what is the weight factor? hint2: how would you compute the internal energy? $\endgroup$
    – Bort
    Commented Jan 15, 2016 at 11:35

1 Answer 1


From these Cornell lecture notes:

Usually we will include the term −μN into the definition of the Hamiltonian Ĥ, so that expressions for the thermal average in the canonical and grand canonical ensembles are formally identical.


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