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I am solving schrodinger and poisson's equation in a self consistent way. I solved schrodinger equation and obtained eigen values which are allowed energy states. now I am calculating electron density with

n=sum(psi*psi*f(E))

where f(E)=1/(1+exp((E-Ef)/kT)) fermi function.

Now I am calculating charge density with carrier densities and putting that in poisson's equation for modified potential.

I am strongly doubtful of calculation of this carrier density n.

My question is, is that single equation is sufficient to account for all electrons in bulk.

though all electrons are identical and indistinguishable, so solution for every electron will be same, but then I think I have to multiply n (above mentioned) with Nn0 which is electron density at equilibrium = ni*ni/Na (for p-type bulk)