The problem of a magnetic impurity, coupled to a metal or a superconducting bath is treated. The system is described using the Kondo model. We formulate the problem, and present the numerical renormalization group method, a standard numerical method in the field. It is employed for calculations of the impurity spectral function, which corresponds to a local density of states. We observe a resonance peak at the Fermi level, which turns out to be typical for the Kondo effect. In the case of the metal bath, we are mostly interested in the behaviour of the resonance peak and its dependence on the impurity energy levels. The Kondo effect fades when we disturb the impurity with a perturbation, comparable in strenght to the coupling energy scale. In the superconducting bath case, focus is on the discrete states that appear in the superconducting gap. Position and splitting of the subgap states is understood using the energy level diagrams of the lowest laying excitations of the system.
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