Three-body and more complicated forces arise since we are dealing with protons and neutrons as effective degrees of freedom. We will come back to this topic later. Furthermore, in large parts of these lectures we will assume that the potential energy can be approximated by a two-body interaction only. Our Hamiltonian reads then $$ \begin{equation} \hat{H} = \sum_{i=1}^A \frac{\mathbf{p}_i^2}{2m_i}+\sum_{ij}^A v(x_i,x_j). \tag{3} \end{equation} $$