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ShuN6211 authored Jan 2, 2023
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Expand Up @@ -23,6 +23,22 @@ $f(E_{q})$ is Fermi distribution function. Solutions in an isolated vortex, espe

<img src="https://latex.codecogs.com/svg.image?\begin{bmatrix}\mathcal{U}_{n}(r,&space;\theta)&space;\\\mathcal{V}_{n}(r,&space;\theta)\end{bmatrix}=\frac{1}{\sqrt{2\pi}}\begin{bmatrix}u_{n}(r)e^{i(n-1)\theta}&space;\\v_{n}(r)e^{in\theta}\end{bmatrix}" title="https://latex.codecogs.com/svg.image?\begin{bmatrix}\mathcal{U}_{n}(r, \theta) \\\mathcal{V}_{n}(r, \theta)\end{bmatrix}=\frac{1}{\sqrt{2\pi}}\begin{bmatrix}u_{n}(r)e^{i(n-1)\theta} \\v_{n}(r)e^{in\theta}\end{bmatrix}" />

$$
\begin{bmatrix}
\mathcal{U}_{n}(r, \theta) \\
\mathcal{V}_{n}(r, \theta)
\end{bmatrix}
=
$$

$$
\frac{1}{\sqrt{2\pi}}
\begin{bmatrix}
u_{n}(r)e^{i(n-1)\theta} \\
v_{n}(r)e^{in\theta}
\end{bmatrix}
$$


Here, $n$ corresponds to angular momentum quantum number, i.e. CdGM mode is characterized by this number. In this library, the range of $n$ is integers of in $[-70, 69]$. Note that the part of $u_{n}(r), v_{n}(r)$ in the right side of above formula is one of the target of this library, not the left side of it.

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