论文标题
潜在散射中的轮廓和表面积分
Contour and surface integrals in potential scattering
论文作者
论文摘要
当研究固定状态的schrödinger方程式针对由$ n $二维欧几里得空间描述的系统所描述的系统时，固定状态的径向部分是参数$λ$的均匀函数，该均值$λ$的均匀函数，这是角动量量子量$ l $ l $ and dimension $ n $ n $ n $ n $ n $。因此，如果不设置先验$ n = 3 $，则可以通过保持$ l $真实并复杂化$ n $来实现$λ$的复杂值。因此，对于这种辅助络合尺寸的合适值，因此可以在散射幅度和相移方面获得结果，这些结果完全等同于$ \ Mathbb {r}^3 $中Yukawian潜力的六十年代获得的结果。此外，如果$ l $和$ n $都复杂化，则可能从两个复杂变量的函数的残基中恢复部分波幅度的可能性。因此，可以将复杂的角动量形式主义嵌入到更广泛的框架中，其中散射振幅与偏斜曲线之间存在$ \ Mathbb {r}^3 $之间的对应关系。
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 $\mathbb{R}^3$.
