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Physics textbook solutions

Physics textbook solutions

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The Hamiltonian of a gas of photons within an empty cavity of volume V is given by the expression
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Consider a gas of non-interacting bosons associated with the energy spectrum
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Consider an ideal gas of bosons with internal degrees of freedom. Suppose that,
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Consider again the same problem for an ideal gas of two- dimensional bosons confined to a surface of area A
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Consider a system of ideal bosons of zero spin (r = 1), within a container of volume V
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Obtain an expression for the magnetic susceptibility asso- ciated with the orbital motion of free electrons in the presence of a uniform magnetic field H,
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In the classical paramagnetic theory of Langevin, pro- posed before the advent of quantum statistics, we assume a classical Hamiltonian, given by
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Consider again the gas of N ultrarelativistic free electrons, within a container of volume V ,
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Consider a system of free fermions in d dimensions, with the energy spectrum
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At low temperatures, the internal energy of a system of free electrons may be written as an expansion
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Consider a gas of N free electrons, in a region of volume V , in the ultrarelativistic regime. The energy spectrum is given by
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Obtain an asymptotic form, in the limit T << TT , for the specific heat of a gas of N free fermions adsorbed on a surface of area A, at a given temperature T
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Show that the chemical potential of an ideal classical gas of N monatomic particles, in a container of volume V , at tem- perature T , may be written as
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