Abstract
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.
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