The discussion centers on the Hydrogen atom problem in statistical mechanics, specifically the divergence of the canonical partition function due to the degeneracy of energy levels represented by E_n = -E_0/n^2. Participants highlight that calculating energies relative to the ground state does not resolve the divergence issue, as it leads to an infinite number of competing non-bound states. The conversation references Landau and Lifshitz's work on quantum mechanics, suggesting that the long-range nature of the Coulomb potential contributes to the instability of isolated bound states in thermodynamic contexts.
PREREQUISITESPhysicists, particularly those specializing in statistical mechanics and quantum mechanics, as well as researchers addressing the stability of atomic systems in thermodynamic contexts.
genneth said:If we are dealing with a canonical ensemble, the extensive variables are S and V; the thermodynamic limit corresponds to holding the conjugate variables T and p constant and letting S and V tend to infinity. The particle number N, is held fixed by definition. If we use a grand canonical ensemble, N is also extensive, and the thing which is held constant is the chemical potential \mu. Your statement about holding the specific volume (i.e. density) constant is equivalent to holding \mu constant in the non-interacting limit, and approximate the same in the weakly interacting limit.
kof9595995 said:I'm not really familiar with these, because all discussions about thermodynamic limit I've read are based on grand canonical ensemble, do you have any online resource about it so that I could read in more details?