  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-$1\over 2$ fermionic partners. The Lorentz invariant
Ansatz for the wave function of the universe, $\Psi$, is taken to be as simple
as possible in order to obtain {\it new} solutions. The wave function has a
simple form when the potential energy term is set to zero. However, neither the
wormhole or the Hartle-Hawking state could be found. The Ansatz for $\Psi$ used
in this paper is constrasted with the more general framework of R. Graham and
A. Csord\'as.
