Quantization of the Bianchi type-IX model in N=1 Supergravity in the Presence of Supermatter

The general theory of N=1 supergravity with supermatter is applied to a Bianchi type IX diagonal model. The supermatter is constituted by a complex scalar field and its spin-$\frac{1}{2}$ fermionic partners. The K"ahler geometry is chosen to be a two-dimensional flat one. The Lorentz invariant Ansatz for the wave function of the universe is taken to be as simple as possible in order to obtain {\it new} solutions. The set of differential equations derived from the quantum constraints are analysed in two different cases: if the supermatter terms include an analytical potential or not. In the latter the wave function is found to have a simple form.