We propose a simple quantum scattering model for particles with arbitrary dispersion relation on point-like impurities. This model generalizes the standard slow particle scattering approximation of quantum mechanics to the anisotropic case. The developed theory is particularly relevant for describing charge carrier dynamics in disordered semiconductors. In the simplest case of a scalar particle, the full energy dependence of scattering cross-section is described through only one real phenomenological parameter analogous to the scattering phase in the s-wave channel. One immediate consequence of our theory is the fact that mean free time is isotropic (independent of the position on the Fermi surface). The model is further extended to a more general case of a multiband spectrum. Energy dependence of the scattering probability is then described in terms of a constant real symmetric matrix whose size corresponds to the number of bands. Finally, we also consider corrections to the scattering properties due to the finite size of impurities. These correctionы are analogous to the p-wave scattering contributions in the isotropic case.