Singular inverse square potential in arbitrary dimensions with a minimal length: Application to the motion of a dipole in a cosmic string background
Singular inverse square potential in arbitrary dimensions with a minimal length: Application to the motion of a dipole in a cosmic string background
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DOI：
10.1103/physreva.78.032110
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发表时间：
2008-09
影响因子：
2.9
通讯作者：
Djamil Bouaziz;M. Bawin
中科院分区：
文献类型：
--
作者：
Djamil Bouaziz;M. Bawin
本文用Heun函数解析求解了量子力学中N维最小长度逆平方势的Schr\ odinger方程。我们将我们的结果应用于宇宙弦背景下的偶极子问题。我们发现，只有当偶极矩与弦之间的夹角大于$\ensuremath{\pi}∕4$时，才存在束缚态。我们将我们的结果与最近文献中相互矛盾的结论进行比较。最小长度可以解释为宇宙弦的半径。
We solve analytically the Schr\"odinger equation for the $N$-dimensional inverse square potential in quantum mechanics with a minimal length in terms of Heun's functions. We apply our results to the problem of a dipole in a cosmic string background. We find that a bound state exists only if the angle between the dipole moment and the string is larger than $\ensuremath{\pi}∕4$. We compare our results with recent conflicting conclusions in the literature. The minimal length may be interpreted as a radius of the cosmic string.