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Although the Kondo effect and the Kondo ground state of a magnetic impurityhave been investigated for more than forty years it was until recentlydifficult if not impossible to calculate spatial properties of the groundstate. In particular the calculation of the spatial distribution of theso-called Kondo cloud or even its existence have been elusive. In recent yearsa new method has been introduced to investigate the properties of magneticimpurities, the FAIR method, where the abbreviation stands for FriedelArtificially Inserted Resonance. The FAIR solution of the Friedel-Anderson andthe Kondo impurity problems consists of only eight or four Slater states.Because of its compactness the spatial electron density and polarization can beeasily calculated. In this article a short review of the method is given. Acomparison with results from the large N-approximation, the NumericalRenormalization Group theory and other methods shows excellent agreement. TheFAIR solution yields (for the first time) the electronic polarization in theKondo cloud.

A Compact Treatment of the Friedel-Anderson and the Kondo Impurity Using the FAIR Method