Kohn anomalies arise together with Friedel oscillations when one considers the Lindhard theory instead of the Thomas–Fermi approximation in order to find an expression for the dielectric function of a homogeneous electron gas. The expression for the real part  of the reciprocal space dielectric function obtained following the Lindhard theory includes a logarithmic term that is singular at , where  is the Fermi wavevector.
Kohn anomalies occur simultaneously with Friedel oscillations when employing the Lindhard theory as opposed to the Thomas-Fermi approximation. This approach yields an expression for the dielectric function of a homogeneous electron gas, featuring a logarithmic term that becomes infinite at , where  is the Fermi wavevector.