I would to check if the following is correct. When integrating the Poisson Eq. once:
dPsi(z)/dz = - integral_0^z (rho(z’)/eps) dz’ + C1
The constant C1 should be C1 = deltaV/L_z (in the finite field method) where deltaV = V_right - V_left is 1.2 V in my case, and L_z the length of the simulation cell in the z direction. Is that correct?
For the second integration (to get Psi(z)) we get C1*z and a second constant C2 (that only produces a vertical shift of the potential, and therefore not physically relevant as you said before).
Thanks