Physics 601: Solid State Physics I
Problem Set #1, due Monday, September 13, 2004 This problem set samples the elementary quantum mechanics and statistical mechanics relevant to solid state physics.

Problem 1: (G. Baym, Lectures on Quantum Mechanics, p. 244, #7)
Estimate the ground state energy of the hydrogen atom using a three-dimensional harmonic oscillator ground state wave function as a trial function. Express your answer in Ry, compare to the exact result, and comment.

Problem 2: Irreversible expansion of a Fermi gas (adapted from C. Kittel, Thermal Physics, 2nd edition, p.259, #10)
Consider a gas of N free noninteracting spin 1/2 fermions of mass M, initially in a volume V_i, thermally insulated from its surroundings, at temperature T _i=0. The density of states is D(E) = (V_i/2pi ²)(2M/hbar²)^3/2E^1/2. Let the gas expand irreversibly into a vacuum, without doing work, to a final volume V_f .
(a) What is the temperature of the gas after expansion if V_f is sufficiently large for the classical limit to apply?
(b) How large should V_f in fact be for the classical limit to apply?