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

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Fluctuations and ComplementsCharacterize the fluctuations of the energy in the grand canonical ensemble and prove that . where .=〈.〉 is the average energy, . the average number of particles, 〈(Δ.).〉 its fluctuations, and 〈(Δ.).〉. the energy fluctuations as obtained from the canonical ensemble.

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Michele Cini,Francesco Fucito,Mauro SbragagliaCarefully written solutions, provide best way to master the subject faster.Theory issues are explained before providing the solution to the exercise.Great number of exercises on different subject cove

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Angular Momentum and Spinind the operator . in spherical polar coordinates and explain why the operators . (azimuthal angle) and . can be measured simultaneously. What are the functions of . whose commutator with . has a physical sense?

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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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https://doi.org/10.1007/978-88-470-2315-4Approximations; Ensembles; Fluctuations; Kinetic theory; Quantum Mechanics

Commodious

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Perturbation Theory and WKB Methodn, determine the off-diagonal elements of the perturbation matrix between the degenerate states. Finally, find the first order correction to the energy of the ground state and the splitting induced on the enery of the first excited state.