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3. (a) Use the two-dimensional density of states expression P(e) = Am/2nh² to obtain the chemical potential m of a non-interacting two-dimensional Fermi gas of N femions occupying an area A at temperature T = 0 K. (b) For T > 0 K, show that the chemical potential is given to a good approximation by H= 8p - kgTln (1+ exp

3. (a) Use the two-dimensional density of states expression P(e) = Am/2nh² to obtain the chemical potential m of a non-interacting two-dimensional Fermi gas of N femions occupying an area A at temperature T = 0 K. (b) For T > 0 K, show that the chemical potential is given to a good approximation by H= 8p - kgTln (1+ exp

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3. (a) Use the two-dimensional density of states expression P(e) = Am/2nh² to obtain the chemical potential m of a non-interacting two-dimensional Fermi gas of N femions occupying an area A at temperature T = 0 K. (b) For T > 0 K, show that the chemical potential is given to a good approximation by H= 8p- kgTln (1+ exp (-)).
Transcribed Image Text:3. (a) Use the two-dimensional density of states expression P(e) = Am/2nh² to obtain the chemical potential m of a non-interacting two-dimensional Fermi gas of N femions occupying an area A at temperature T = 0 K. (b) For T > 0 K, show that the chemical potential is given to a good approximation by H= 8p- kgTln (1+ exp (-)).
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