1. Preface: I derived the quantum length, l_Q  for a quantum mechanical particle (e.g. an electron, an atom, etc.) in class. The quantum volume per particle is thus v_Q=l_Q³. There is an approximate boundary between the classical world of "big things" and the quantum world of "small things." The classical volume per particle is given by the usual V/N, while that in the quantum world is v_Q. The boundary between the two worlds is achieved when V/N≈v_Q; things are classical when V/N>>v_Q and quantum when V/N≈v_Q or V/N<v_Q.
   Problem: work problem 7.9.
2. problem 7.11. Let the "room temperature" T=295K for consistency.
3. problem 7.13. Again, let T=295K for consistency.
4. For fermions, graph the probability of a single state being occupied, <n> for energies 0eV<ε<0.20eV. Let the chemical potential μ=0.050eV. Do this on one graph for the 5 temperature values T=3K, 30K, 300K, 3,000K and 30,000K. Do this in Maple, not by hand. Label (by hand, if necessary) which curve corresponds to which temperature.
5. For bosons, graph the probability of a single state being occupied, <n> for energies 0.0501eV<ε<0.100eV. Let the chemical potential μ=0.050eV. Do this on one graph for the 5 temperature values T=3K, 30K, 300K, 3,000K and 30,000K. Do this in Maple, not by hand. Let the y-values (<n>-values) range from 0 to 100 (use the command y=0..100 to do this). Label (by hand, if necessary) which curve corresponds to which temperature.

I found that you can have different styles of lines using the option linestyle=[1,1,2,3,4] in Maple's plot() command. As it says on the Maple Help pages, the numbers 1, 2, 3, and 4 correspond to things likes dashes, dash-dots, etc. Play around with this to see what's going on so that you can clearly understand what the temperature does to the graphs. Or, you can put in the options SOLID, DOT, DASH or DASHDOT intead of these numbers.

Note: You can write the three particle occupancy distributions (Fermi-Dirac, Bose-Einstein, and Boltzmann) as <n>=(exp[-β(ε-μ)]+a)^-1 where where a=+1 for Fermi-Dirac, a=0 for Boltzmann, and a=-1 for Bose-Einstein statistics.

That's all for homework #9.

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