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2 dimension free electron gas N noninterecting electron at T=0 restricted inside a square of length L.

A) what are the energy eigenvalue of each electron?

B)How many available quantum states are there for electron whose maximum is less than a certain maximum value of P?

C) find the formula for Fermi energy of system

D) If the number density is n = 50/nm^2, find the value of Ef in eV.(MeC^2 = 0.511 MeV)

E) Suppose T is not 0 but low Cu->aT^n. Find n.

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