## 1 Introduction  
To design nanoelectronic devices from 2D materials, it is important to precisely understand the dynamics of electrons in these structures. While Bloch waves propagate freely in the perfect crystal, in the presence of defects [1, 2, 3] the quasi-particles will be scattered and interfered with themselves, which will influence the transport properties of the material [4, 5, 6]. The interference of incoming and scattered waves leads to characteristic patterns in the local density of states (LDOS) around the defects, called quasiparticle interference (QPI) patterns [7, 8] also referred to as Friedel oscillations [9]. The investigation of the QPI patterns around defects not only gives information on the type of the impurity, but also on more hidden band structure properties of the host material. A prime example of graphene, where the chiral property of the Dirac electrons has a substantial effect on the scattering processes [10]. In graphene two main types of scattering processes are possible: intravalley scattering within one \(K\) (\(K^{\prime}\)) valley or intervalley scattering between two neighboring \(K\) and \(K^{\prime}\) valleys. Due to the honeycomb structure of the graphene lattice, a new degree of freedom, the pseudospin, emerges. It was proved earlier that the conservation of pseudospin during the scattering process leads to suppression of intravalley backscattering resulting in a topological fingerprint in the QPI patterns. Experimentally, the real-space modulation of the LDOS is accessible by fast Fourier transformation (FFT) of the topography or tunneling conductance maps, measured by scanning tunneling microscopy [11]. The great advantage of the STM is that it allowsus to understand the basic mechanism of quasiparticle scattering at the atomic scale. By using this method, the quasiparticle chirality effects were observed in graphene [12; 13; 14]. However, the experimentally observed QPI often has complicated patterns because the elastic scattering mixes states that are located on the same quasiparticle contour of constant energy (CCE). If the material has an intricate Fermi surface, where multiple scattering effects can take place, the measured FFT-STS images display more complex characters and theoretical investigations are highly necessary to understand the experiments [15; 16]. Wave packet dynamics (WPD) [17] can simulate electronic dynamics including multiple scattering processes at the nanoscale and are capable of calculating realistic models containing several hundred atoms already on a personal computer. The physical system is described by a Hamiltonian and the initial conditions are given by an initial wave function. Solution of the time-dependent Schrodinger equation then yields the \(\psi\left(\overset{\rightarrow}{r},t\right)\) time-dependent wave function and its time-energy Fourier transform gives the \(\psi\left(\overset{\rightarrow}{r},E\right)\) energy-dependent wave function, which can be used for the interpretation of the QPI patterns measured by STM. In the one particle approximation, we calculate only a one (quasi)particle three-dimensional (3D) wave function instead of the 3N dimensional many-body wave function and the details of the many-body interactions are coded into the Hamilton operator. This can be achieved by building an appropriate \(V\left(\overset{\rightarrow}{r}\right)\) one-particle pseudopotential. During the past decade we were performing WPD calculations [18; 19; 20] for many sp\({}^{2}\) carbon nanosystems by using a variationally calculated local carbon one-electron pseudopotential [21]. This pseudopotential has two major advantages: (i) it brings the specific electronic dynamics of the bands (linear dispersion near the \(K\) points for electrons near the Fermi energy (E\({}_{\text{F}}\)), trigonal warping for hot electrons, etc.) into the WPD calculation and (ii) it allows us to handle localized defects. We were able to exploit this feature of the pseudopotential in calculating the transport properties of different 0D and 1D graphene defects [22; 23].