应用条件形状不变性对称性求混合势V（r）= ar + br^2 + c/r + l（l+1）/r^2的本征谱
Application of conditional shape invariance symmetry to obtain the eigen-spectrum of the mixed potential V (r) = ar + br^2 + c/r + l(l+1)/r^2
摘要：
我们证明了条件形状不变性对称性可以作为一个非常强大的工具来计算混合势V（r）= ar + br^2 +c/r + l（l+1）/r^2的本征值。任何状态的能量都可以用代数方法得到，尽管势参数的集合受到严格的限制。我们还指出，汉密尔顿层次中的每个成员基本上是条件平移形状不变的。分析得到的结果与数值结果的比较。本文的方法可作为计算条件精确可解（CES）势的任意高阶激发态的另一种方法。
英文摘要：
We show that the conditional shape invariance symmetry can be used as a very powerful tool to calculate the eigenvalues of the mixed potential V (r) = ar + br^2 +c/r + l(l+1)/r^2 for a restricted set of potential parameters. The energy for any state can be obtained algebraically, albeit for a severely restricted set of potential parameters. We also indicate that each member of the hierarchy of Hamiltonians is basically conditionally translational shape invariant. Comparison of analytically obtained results with numerical results is also presented. Our present methodology can be taken as an alternative treatment for the calculation of any higher order excited states of conditionally exactly solvable (CES) potentials.
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