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QUESTION

when f_0 (p)=exp⁡(〖(E〗_f-E_c )/k_B T).exp⁡(-p^2/2m^* k_B T) proof equation J^+=ℏq/(3π^2 m^* ) k_f^3=(2q√(2m^* ))/(3π^2 ℏ^2 ) (E_f-E_c )^2

when 

f_0 (p)=exp⁡(〖(E〗_f-E_c )/k_B T).exp⁡(-p^2/2m^* k_B T)

proof equation

J^+=ℏq/(3π^2 m^* ) k_f^3=(2q√(2m^* ))/(3π^2 ℏ^2 ) (E_f-E_c )^2 

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