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hw10 - PHYS 333 Winter 2009 Assignment 10 Due 5:00 pm...

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PHYS 333 Winter 2009 Assignment 10 Due: 5:00 pm Friday April 17 1. Schroeder 7.16 A system of N (spinless) identical fermions has equally spaced energy levels which are all non-degenerate. (That is, each level holds only one fermion.) At low temperatures, it is useful to represent each state of the system by a column of dots, where a filled dot represents an occupied level, and an open dot represents an un-occupied level. At low temperatures, all states below a certain level are occupied, and are not shown on the dot-diagram. Suppose that the spacing between the levels is η , and that q is the number of energy units over and above the ground-state energy U 0 . That is, the (internal) energy is U = U 0 + . The figure shows all possible states for 0 q 3. q = 0 1 2 3 (a) Draw dot-diagrams for q = 4 , 5 and 6. (b) Compute, therefore, the probability of each level being occupied when q = 6. Plot a graph of this probability as a function of the energy of each level, and from the graph, estimate μ and T by “fitting” to the Fermi-Dirac distribution.
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