We performed wave packet dynamical calculations for graphene‐ and MoS2 monolayers by a new formulation of the split‐operator FFT method utilizing ab initio band structure results into the kinetic energy operator. While the time dependent dynamics is available through the solution of the time dependent Schrödinger equation in wave packet dynamics, the energy dependent dynamics is calculated by the application of the time–energy Fourier transform to the wave function. Time dependent probability results show an anisotropic spreading of the probability density current. The magnitude and angular dependence of the anisotropy is dependent (i) on the process creating the initial wave packet (e.g., injection from an STM tip or scattering on an impurity) and (ii) on the details of the band structure.