Abstract
The Finite Difference Time Domain method has been used to find the angular excited states wave functions in two dimensions. These excited states are calculated by applying the iterative procedure on a specified initial guess wave function that contains the desired excited state as a lowest state, this is simply done by introducing lines of zeros in the wave functions and their second derivatives. This of course depends on the symmetry of the potential. We choose here either square or cylindrical symmetry, so the lowest angular excitations will contain lines of zeros one or two passing through the region, namely, the first excited state and the second excited state respectively. In our investigation, we apply this technique to two simple potentials, which are the two dimensional simple harmonic oscillator and the finite cylindrical well potential in order to illustrate the accuracy and the efficiency of these calculations. These potentials were chosen, as the analytical solutions are available, so to compare them with our results using MATLAB program