（反）de Sitter空间中氢原子的薛定谔方程的精确解
Exact Solution of Schrödinger Equation in (Anti-)de Sitter Spaces for Hydrogen Atom
摘要：
利用推广的不确定原理，我们在de Sitter和Anti-de Sitter空间中写出了库仑势的薛定谔方程.我们使用Nikiforov-Uvarov方法来求解方程。两个系统的能量本征值以其精确形式给出，对应的径向波函数在de Sitter空间用Jacobi多项式表示，而Anti-de Sitter空间用Romanovski多项式表示.我们还研究了在这两种情况下空间形变参数对束缚态的影响。
英文摘要：
We write Schrödinger equation for the Coulomb potential in both de Sitter and Anti-de Sitter spaces using the Extended Uncertainty Principle formulation. We use the Nikiforov-Uvarov method to solve the equations. The energy eigenvalues for both systems are given in their exact forms and the corresponding radial wave functions are expressed in associated Jacobi polynomials for de Sitter space, while those of Anti-de Sitter space are given in terms of Romanovski polynomials. We have also studied the effect of the spatial deformation parameter on the bound states in the two cases.
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