Please print this sheet, sign the statement at the bottom, and use it as cover page when you submit your homework. Remember to always include a complete explanation of your reasoning, and to show all calculations.

• 1: Neutrons in a Box [from Kennett, Problem 4.8]
  Consider ultra-cold dilute neutrons, at temperature T = 1 mK, which are initially placed at the bottom of a box of height H. How high does the box need to be to ensure that a neutron with energy equal to the mean energy at that temperature remains in the box?

• 2: Harmonic Oscillator Entropy [from Kennett, Problems 4.13 and 4.14]
  Calculate the entropy S and energy U for a 1D harmonic oscillator of mass m and spring constant k at temperature T, and hence determine its heat capacity C. Do this for (a) a quantum and (b) a classical oscillator, and in each case comment on whether your answer agrees with what you expect from the equipartition principle.

• 3: Density of States in Two Dimensions [adapted from Kennett, Problem 7.2]
  Find the density of states g(E) for (a) massive particles and (b) massless particles, in two spatial dimensions. Compare the energy dependence to the result for the three-dimensional case that we found in class.

Aside from oral discussions I may have had with other students in the class, the solutions to this homework set I am submitting are entirely my own, and I did not use anyone else's worked out solution to any of these problems when writing mine.

Signed:   _______________________________________