= Finite-width quantum-well exciton
{title2=$V(\rho)=-\frac{e^2}{4\pi\epsilon_0\epsilon_r}\int\frac{|\chi_e(z_e)|^2|\chi_h(z_h)|^2}{\sqrt{\rho^2+(z_e-z_h)^2}}\,dz_e\,dz_h$}
In the envelope approximation, a <quantum well> confines <electron> and <hole> motion perpendicular to the plane. Averaging their screened attraction over the confinement envelopes gives the displayed effective in-plane potential. Its narrow-well limit approaches the ideal <two-dimensional exciton>; finite width softens the short-distance attraction. Dielectric mismatch, nonparabolic bands and strong <electron>–<hole> confinement mixing require more than this single-subband model.
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