Self-Consistent Solution of the Anderson Model

The Anderson model is studied by means of retarded double-time Green's functions in the limit $U\to \infty$. Using a truncation procedure and solving self-consistently for the averages, an integral equation for the transition matrix is derived. The exact solution to this equation can be found by analytic methods and is very similar to the solution to the $s-d$ exchange model. The known perturbation result for high temperatures is also obtained from our integral equation.