3) [30 points total] Consider a gas of N identical, non-relativisti...

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3) [30 points total] Consider a gas of N identical, non-relativistic, non-interacting spin 1/2 fermions (spin degeneracy 9s = 2), confined to move in a one-dimensional system of length L. a) [10 pts] The density of states, g(€), is defined as the number of single-particle states with energy € per unit energy per unit length. Compute g(e) for the gas. b) [10 pts] Compute the Fermi energy of the gas as a function of its density n = N/L. c) [10 pts] Compute the pressure of the gas at T = 0 as a function of its density n.

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