D维赝谐势加环形势的薛定谔方程的精确解
Exact solutions of the Schrodinger equation in D-dimensions for the pseudoharmonic potential plus ring-shaped potential
摘要：
本文利用Nikiforov-Uvarov方法，对赝谐势加上$V(r,θ)=D_{e}(\frac{r}{% r_{e}}-\frac{r_{e}}{r}) ^{2}+\frac{β\cos ^{2}θ}{r^{2}\sin ^{2}θ}$形式的环形势，解析地给出了$D$维薛定谔方程的能量束缚态精确解.我们还给出了一个明确的配方，如何获得一个明确的解决方案的径向和角度部分的波函数的正交多项式。由于角部分的贡献，系统的总能量与赝谐势不同。在这项工作中得到的一般结果可以减少到文献中给出的标准形式。
英文摘要：
We present analytically the exact energy bound-states solutions of the Schrodinger equation in $D$-dimensions for a pseudoharmonic potential plus ring-shaped potential of the form $V(r,θ)=D_{e}(\frac{r}{% r_{e}}-\frac{r_{e}}{r}) ^{2}+\frac{β\cos ^{2}θ}{r^{2}\sin ^{2}θ}$ by means of the conventional Nikiforov-Uvarov method. We also give a clear recipe of how to obtain an explicit solution to the radial and angular parts of the wave functions in terms of orthogonal polynomials. The total energy of the system is different from the pseudoharmonic potential because of the contribution of the angular part. The general results obtained in this work can be reduced to the standard forms given in the literature.
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