最小长度的Hartmann势与矩阵元的广义递推关系
Hartmann potential with a minimal length and generalized recurrence relations for matrix elements
摘要：
本文利用广义不确定原理研究了Hartmann势下的薛定谔方程。我们微扰地得到了变形参数$β$中一阶哈密顿量的矩阵元，并证明了一些简并态被去除。我们给出了对角矩阵元素解的解析表达式。最后，我们导出了角平均值的广义递推公式。
英文摘要：
In this work we study the Schrödinger equation in the presence of the Hartmann potential with a generalized uncertainty principle. We pertubatively obtain the matrix elements of the hamiltonian at first order in the parameter of deformation $β$ and show that some degenerate states are removed. We give analytic expressions for the solutions of the diagonal matrix elements. Finally, we derive a generalized recurrence formula for the angular average values.
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