Abstract
In this paper, we exactly solve the Wheeler-DeWitt equation in the presence of a conformally coupled scalar field and in the context of the generalized uncertainty principle (GUP). The GUP-corrected Wheeler—De Witt equation in momentum space leads us to introduce factorization method. This method helps us to obtain the exact solution for the corresponding system. So, here we factorize the second-order equation in terms of first-order operators. These first-order operators help us to arrange partner potential and superpotential. Also, we achieve the general quantum stats and energy spectrum for GUP with conformally coupled scalar field system. Also, we show that the stability of a system with the energy spectrum with some conditions.
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