Determining which wave functions contribute to the ground state formation of the solid is key to determining electronic and optic properties of quantum materials. However, few experimental techniques allow to directly measure the orbital composition of the ground state, in particular for strongly correlated materials with partially filled d shells. A novel experimental technique, non-resonant inelastic x-ray scattering (NIXS), promises exactly that: Imaging the orbitals in quantum materials directly in real-space. In this Master thesis, we propose to calculate the NIXS cross section of a transition metal oxide, CuO, based on state-of-the art many-body simulations. We will use a combination of ab initio density functional theory and dynamical mean-field theory to describe the electronic structure of the material. Building on a recently developed cluster solver, we will calculate in a second step the NIXS cross section, which amounts at the M1-edge to a quadrupolar transition from the core 3s-shell to the valence 3d-shell of copper.