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Titlebook: Solved Problems in Quantum and Statistical Mechanics; Michele Cini,Francesco Fucito,Mauro Sbragaglia Textbook 2012 Springer-Verlag Italia

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Grand Canonical Ensembleion of the average number of particles 〈.〉 which are adsorbed by the surface. You can think that the canonical partition function of an adsorbed molecule is a function only of the temperature, .(.), and that all the adsorbed molecules are non interacting.
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Fermi-Dirac Gasesits nature at the ambient temperature. Assume that the particles are independent with a single particle energy . where . is the absolute value of the momentum. Also, make use of: .=7×10.GeVS, 10.cm≈7×10.s, .=8.61×10.eV/K
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Thermodynamics and Microcanonical EnsembleGiven this result, from the differential properties of .(.), show that . with Φ the Gibbs potential defined as Φ=.+.. In the above expression, μ is the chemical potential properly defined in terms of .(.).
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Kinetic Physicsf volume .. Treat the general case with a single particle energy ε=ε(.), i.e. only dependent on the absolute value of the momentum. Also, determine the pressure and discuss the corresponding classical limit. Finally, discuss the case of a photon gas with a single particle energy . and a chemical pot
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