arXiv 2001.112172020-01hep-thquant-ph

势散射中的轮廓积分和曲面积分

Contour and surface integrals in potential scattering

Giampiero Esposito

备注：: 11 pages; the line after Eq. (1.1), and two misprints, have been amended

摘要：

在$n$维欧氏空间中研究中心势描述的定态薛定谔方程时，定态的径向部分是参数$λ$的偶函数，参数$λ$是角动量量子数$l$和维数$n$的线性组合，即，$λ=l+{(n-2)\over 2}$。因此，在不设置先验$n=3$的情况下，可以实现$λ$的复值，特别是通过保持$l$为实并且使$n$复化。对于这样一个辅助复杂化的尺寸的合适的值，因此，它是可能的散射振幅和相移的结果是完全等效的结果在六十年代获得的Yukawian势在$\mathbb{R}^3$。此外，如果$l$和$n$都是复化的，则出现了从两个复变量的函数的残差恢复分波振幅的可能性。因此，复杂的角动量形式主义可以嵌入到一个更广泛的框架，在散射振幅和$\mathbb{R}^3$中的偏斜曲线之间存在对应关系。

英文摘要：

When the Schrödinger equation for stationary states is studied for a system described by a central potential in $n$-dimensional Euclidean space, the radial part of stationary states is an even function of a parameter $λ$ which is a linear combination of angular momentum quantum number $l$ and dimension $n$, i.e., $λ=l+{(n-2)\over 2}$. Thus, without setting a priori $n=3$, complex values of $λ$ can be achieved, in particular, by keeping $l$ real and complexifying $n$. For suitable values of such an auxiliary complexified dimension, it is therefore possible to obtain results on scattering amplitude and phase shift that are completely equivalent to the results obtained in the sixties for Yukawian potentials in $\mathbb{R}^3$. Moreover, if both $l$ and $n$ are complexified, the possibility arises of recovering the partial wave amplitude from residues of a function of two complex variables. Thus, the complex angular momentum formalism can be imbedded into a broader framework, where a correspondence exists between the scattering amplitude and a skew curve in $\mathbb{R}^3$.

机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。

摘要：

英文摘要：

相关论文