We first present a new constraint condition on the confluent Heun function H _C (α , β , γ , δ , η ;z ) (β , γ  ≥ 0, z ∈ [0, 1]) and then illustrate how to solve the rigid rotor in the electric field. We find its exact solutions unsolved previously through solving the Wronskian determinant. The present results compared with those by the perturbation methods are found to have a big difference for a large parameter a . We also present 2D and 3D probability density distributions by choosing different angular momentum quantum numbers l . We observe that the original eigenvalues with degeneracy (2 l  + 1) are split into the (l  + 1) state with approximate eigenvalues l (l  + 1) for small a but large l .

中文翻译：

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刚性转子在电场中的精确解

我们首先提出在汇合休恩函数一个新的约束条件ħ _Ç（α，β，γ，δ，η ; Ž）（β，γ  ≥0，ž ∈[0，1]），然后示出了如何解决所述刚性转子在电场中。通过求解Wronskian行列式，我们发现以前无法解决的确切解决方案。与摄动法相比，目前的结果对于大参数a具有很大的差异。我们还通过选择不同的角动量量子数来表示2D和3D概率密度分布l。我们观察到，具有简并性（2 l  +1）的原始特征值被分解为（l  +1）状态， 对于小a但大l则具有近似特征值l（l +1）。