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(Computational problem. It would help to have a spreadsheet or a programmable calculator.) Consider a system of bosons at 290 K with µ = -0.01 eV, for which the energies of the various states are given by εm = m0.01 eV, where m = 0, 1, 2, 3,...
(a) What is the total number of particles in this system, on average?
(b) What is the total energy of this system, on average?
(c) Repeat parts (a) and (b) for the case where the mth state is m + 1 times degenerate.
Assume all deflections to be small (e.g., m moves approximately vertically if θ is small), and neglect gravity. Use the Extended Hamilton's Principle to derive the equations of motion and the boundary conditions for this system.
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