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Do both KK 7.11 and 7.12: fun with number fluctuations in Fermi and Bose gases.
(See what a different statistics makes!)
Assume that your particles of gas live in one dimension. Also assume
that they
are relativistic: they obey
E=hc|n|/(2L).
(a) Derive curly D1 , the
density of states in energy space, for one-dimensional non-interacting
gases with a translational degree of freedom.
(b) Assuming that
the particles are spin-half fermions, find the zero-temperature
physics, and the heat capacity at low-T, of a Fermi Gas.
(c) Now,
instead, assume that the particles are spin-zero bosons. Figure out
the physics of Bose-Einstein condensation in this system, i.e. the
fraction of particles in the groundstate at low-T.
Do KK 7.6 on the mass-radius relationship for [non-relativistic] white dwarfs, and then KK 7.10 on relativistic white dwarfs.
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