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 Re ⁡ ⁡ ( ε ε ( q , ω ω ) ) of the reciprocal space dielectric function obtained following the Lindhard theory includes a logarithmic term that is singular at q = 2 k F , where k F is the Fermi wavevector. Although this singularity is quite small in reciprocal space, if one takes the Fourier transform and passes into real space, the Gibbs phenomenon causes a strong oscillation of Re ⁡ ⁡ ( ε ε ( r , ω ω ) ) in the proximity of the singularity mentioned above. In the context of phonon dispersion relations, these oscillations appear as a vertical tangent in the plot of ω ω 2 ( q ) , called the Kohn anomalies.