a) Consider two single-particle energy states of the fermion system, A and B, for which EA = μ-x and EB = μ + x. Show that the probability that state A is occupied is equal to the probability that state B is unoccupied. In other words, show that the Fermi and Dirac distribution, f(E)= 1 eß(E-μ) +1 is "symmetric" about the point E = μ. b) Write simplified, approximate expressions for f(E) when value of E is very close to μ. (i) E < μ, (ii) E»μ " and (iii) the
a) Consider two single-particle energy states of the fermion system, A and B, for which EA = μ-x and EB = μ + x. Show that the probability that state A is occupied is equal to the probability that state B is unoccupied. In other words, show that the Fermi and Dirac distribution, f(E)= 1 eß(E-μ) +1 is "symmetric" about the point E = μ. b) Write simplified, approximate expressions for f(E) when value of E is very close to μ. (i) E < μ, (ii) E»μ " and (iii) the
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Transcribed Image Text:a) Consider two single-particle energy states of the fermion system, A and B, for which EA = μ- x
and EB = μ + x. Show that the probability that state A is occupied is equal to the probability that
state B is unoccupied. In other words, show that the Fermi and Dirac distribution,
ƒ(E)
1
eß(E-μ) +1
is "symmetric" about the point E = μ.
b) Write simplified, approximate expressions for f(E) when
value of E is very close to μ.
(i) E < µ, (ii) E» µ
2
and (iii) the
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