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You are right, that the medium is made of quantum systems which have to be treated accordingly. When you consider every individual molecule/atom in your material the induced polarization at that individual molecule/atom is given by the induced dipole moment $d(t)$, which is well defined via $$d(t) = \langle \psi(t) | \hat d | \psi(t) \rangle,$$ where $\... 1 The dipole is symmetric about its axis, hence the azimuthal symmetry. If the dipole is oriented along$\hat z$(as it done usually) and one uses cylindrical coordinates with$\hat z$as the axis of the cylinder, it is clear geometrically that points at constant height$z$and constant$\rho=\sqrt{x^2+y^2}\$, i.e. point in a plane perpendicular to the axis ...