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The "Relativistic Modified Augmented Plane Wave" (RMAPW) method of Bross and Hofmann (1969) was realized numerically in a slightly modified form and tested with the example of copper potential of Burdick (1963). With regard to future applications in the area of surface-bandstructures and surface-states this realization was done in a generalization of the RMAPW-method for complex k-vectors ("complex RMAPW") of Wachutka (1978).\n\nStarting from the "Overlapping Charge Density" (OCD) potential of gold in "Muffin Tin" (MT) form from Christensen and Seraphin (1971) in this work a selfconsistent gold potential in "Warped Muffin Tin" (WMT) form was computed. As a modell for the electron-electron interaction the effective local single-particle-potential in the context of the "Local Density Approximation" (LDA) with relativistic adjustments for the exchange-term of MacDonald and Vosko (1979) was used.\n\nOn the basis of the energy spectrum, the density of states, and the anisotropy of the fermi-surface the approximations of WMT and DFF/LDA are discussed. The most essential result is, that with the selfconsistent potential there is in the energy-scale a movement of the occupied d-bands slightly upwards and a broadening of the d-bandwidth, in contrast to some experiments. Neddermeyer (1981) suggested a drastic upshift of the 7. band - for that proposal there is no evidence in this work.\n\nBecause in this calculation exchange- and correlation-potentials are free from adjustable parameters, the author guesses, that in the difference between theory and experiment we have reached the limit of the local approximation (LDA).\n\nThis publication is 99% identical with the PhD-thesis of the author at LMU Munich in March 1984. Minor add-ons are given in brackets [...].\n\nA new appendix from 2012 adds some informations from the assets of the author and discusses some interesting newer PhD-theses about Copper and Gold, done at the Institut of Theoretical Solid State Physics (Prof. H. Bross) at LMU Munich.