  We study the quantum cosmology of the 2D Hawking-Page massless scalar-field
model and the homogeneous and isotropic dilation-axion string cosmology.For
both models we find new exact solutions for the Wheeler-DeWitt equation and for
the supersymmetric wave function equations. We show that the Wheeler-DeWitt
equations for the Hawking-Page model and the axion-dilaton string cosmology are
invariant under a one-parameter and two-parameter squeezed transformations,
respectively. These results allow to find new solutions for the wave functions
of these systems at the quantum cosmology level. Also, we apply the same
squeezed transformations to solve the supersymmetric wave equations and find
new supersymmetric solutions for the 2D Hawking-Page massless scalar-field
model and the homogeneous and isotropic dilation-axion fields. Besides, for the
former case, with the help of separation of variables we find new
supersymmetric wave functions.
