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首页> 外文期刊>Journal of atomic and molecular physics >Solutions to the Schr?dinger Equation with Inversely Quadratic Yukawa Plus Inversely Quadratic Hellmann Potential Using Nikiforov-Uvarov Method
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Solutions to the Schr?dinger Equation with Inversely Quadratic Yukawa Plus Inversely Quadratic Hellmann Potential Using Nikiforov-Uvarov Method

机译：用Nikiforov-Uvarov方法解带逆二次Yukawa加逆二次Hellmann势的Schr？dinger方程

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摘要

The solutions to the Schr?dinger equation with inversely quadratic Yukawa and inversely quadratic Hellmann (IQYIQH) potential for any angular momentum quantum number l have been presented using the Nikiforov-Uvarov method. The bound state energy eigenvalues and the corresponding unnormalized eigenfunctions are obtained in terms of the Laguerre polynomials. The NU method is related to the solutions in terms of generalized Jacobi polynomials. In the NU method, the Schr?dinger equation is reduced to a generalized equation of hypergeometric type using the coordinate transformation s = s(r).The equation then yields a form whose polynomial solutions are given by the well-known Rodrigues relation.With the introduction of the IQYIQH potential into the Schr?dinger equation, the resultant equation is further transformed in such a way that certain polynomials with four different possible forms are obtained. Out of these forms, only one form is suitable for use in obtaining the energy eigenvalues and the corresponding eigenfunctions of the Schr?dinger equation.
机译：已经使用Nikiforov-Uvarov方法给出了具有逆二次Yukawa和逆二次Hellmann（IQYIQH）势的Schr？dinger方程对于任何角动量量子数l的解。结合状态能量本征值和相应的未归一化本征函数是根据Laguerre多项式获得的。 NU方法与广义Jacobi多项式的解相关。在NU方法中，使用坐标变换s = s（r）将Schr？dinger方程简化为超几何类型的广义方程，然后该方程产生一种形式，该形式的多项式解由众所周知的Rodrigues关系给出。将IQYIQH势引入Schrdinger方程后，对所得方程进行进一步转换，以获得具有四种可能形式的某些多项式。在这些形式中，只有一种形式适合用于获得Schr？dinger方程的能量本征值和相应的本征函数。

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