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.

中文翻译：

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具有超对称量子力学的宇宙学中的广义不确定性原理

摘要

在本文中，我们在存在共形耦合标量场和广义不确定性原理（GUP）的情况下，精确求解了Wheeler-DeWitt方程。动量空间中经GUP校正的Wheeler-De Witt方程使我们引入分解方法。这种方法有助于我们获得相应系统的精确解决方案。因此，这里我们根据一阶算子对二阶方程进行分解。这些一阶运算符可帮助我们安排合作伙伴的潜力和超潜力。此外，我们利用保形耦合标量场系统获得了GUP的一般量子统计和能谱。同样，我们证明了在某些条件下具有能谱的系统的稳定性。