1. The density of copper is 8.96 g/cm³ and its atomic weight is 63.5 g/mole.
(a) Calculate the Fermi energy for copper assuming one conduction electron per atom.
(b) What is the speed of an electron at the Fermi level? Is the non-relativistic approximation (using Schrödinger’s instead of Dirac’s equation) valid?
(c) What is the Fermi temperature? Can room temperature be considered to be approximately absolute zero in comparison?
(d) What is the electron degeneracy pressure?

2. Experimental measurements of the heat capacity of aluminum at low temperatures (below about 50 K) can be fit to the formula CV = +bT³ where CV is the heat capacity of one mole of Al, a = 0.00135 J/K², and b = 2.48 × 10−5 J/K⁴. Find a formula for the entropy per mole of Al in terms of temperature. What is the entropy of 1 gram of Al at 3K? (The linear piece of CV is due to the conduction electrons and the cubic piece is due to phonons.)

3. An electron is trapped in a 3-dimensional box 1 fm on a side (about the size of a nucleus). Find the six lowest distinct energy levels in eV. For each energy level, list its degeneracy; that is, how many different states have the same energy?

4. Show that adding a constant V0 to the potential energy V (x) in Schrödinger’s equation changes the wave function by a phase exp(−iV0t/h ̄). This phase has no effect on the expectation value of any dynamic variable (any variable that depends on position x and momentum p) and thus can not be seen experimentally.

5. In problem 4 above, find an accidental degeneracy. That is, find two sets of three integers (nx,ny,nz) whose squares sum to the same constant. Hint: it occurs first in the 14th energy level.

1. The density of copper is 8.96 g/cm³ and its atomic weight is 63....