  Solving the single-impurity Anderson model (SIAM) is a basic problem of solid
state physics. The SIAM model is very important, at present it is also used for
systems with quantum impurities, e.g. semiconductor quantum dots and molecular
transistors. Its main application is in the scheme of dynamical mean field
theory (DMFT) describing strong correlation electron systems. To solve the SIAM
problem we use the equation of motion (EOM) Green function approach. In this
report we present the novel EOM approximation in which we differentiate the
Green function over both time variables. This differs from the commonly used
EOM solution by Appelbaum, Penn and Lacroix where the authors take time
derivative only over primary time variable. After extending calculations to
higher order Green functions we find the new approximate dynamical solution of
SIAM. The results are compared with the solutions to the SIAM problem at
intermediate Coulomb repulsion U such as the Modified Iterative Perturbation
Theory. Our approach is suitable for describing quantum dots.
