Consider a classical ideal gas of N indistinguishable, non-interacting, particles confined to a
region of three dimensional space by a harmonic potential V(r). This might be a model for
a gas of atoms in a magnetic trap. The single particle Hamiltonian is then,
a) [10 pts] Compute the average total energy E of the gas as a function of temperature T.
Compute the total specific heat C.
b) [10 pts] Compute the density of particles n(I) at position r. Note, n(r) should be nor-
malized SO that j dr = N.
c) [5 pts] What is the root mean square distance
(r2) of particles from the origin?
d) [5 pts] What is the pressure of the gas p(r) at a position r?
e) [10 pts] What is the chemical potential of the gas H(I) at position r?
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