Using different modifications of a new variational approach, statical
groundstate properties of the one-band Hubbard model such as energy
and staggered magnetisation are calculated. By taking into account
additional fluctuations, the method ist gradually improved so that a
very good description of the energy in one and two dimensions can be
achieved. After a detailed discussion of the application in one dimension, extensions for two dimensions are introduced. By use of a modified
version of the variational ansatz in particular a description of the
quantum phase transition for the magnetisation should be possible.