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The probability for occupying the Fermi level PF = 1/2. If the probability for occupying a level ΔE above EF is P+

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The probability for occupying the Fermi level PF = 1/2. If the probability for occupying a level ΔE above EF is P+ and that for a level ΔE below EF is P−, then show that for ΔE/kT << 1, PF is the mean of P+ and P−

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∴ (P+ + P−)/2 = 1/2 = PF

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