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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 ?
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.
