In the case of the hydrogen atom, we have the discrete spectrum, meaning that the permissible values of energy levels E form a well-separated energetic ladder. However, for metals or semiconductors (i.e. complex, extended systems) that are of particular interest when considering Friedel oscillations, these levels merge into conduction and valence bands. The spectrum of the Hamiltonian for such systems is continuous. Our simple free electron gas model has a continuous spectrum, and in general, if we have a very finely combed discrete spectrum, it is simply replaced with a continuous one, as integration is less painful than summation.