数学公式渲染测试

G(\omega) = \frac{1}{\omega - H - \Sigma(\omega)}

\varepsilon_{\boldsymbol{k}} = \frac{\hbar^2 |\boldsymbol{k}|^2}{2m} - \mu

\rho(E) = \frac{1}{N_k} \sum_{n,\boldsymbol{k}} \delta\!\left(E-\varepsilon_{n\boldsymbol{k}}\right)

\int_{-\infty}^{+\infty} e^{-a x^2}\,\mathrm{d}x = \sqrt{\frac{\pi}{a}}, \qquad a>0

\sqrt{x}, \quad \sqrt{\frac{\pi}{a}}, \quad \sqrt[3]{x^2+y^2}, \quad \sqrt{\frac{\alpha+\beta}{\gamma+\delta}}

\char"221A x, \quad \sqrt{x}, \quad \sqrt{x+y+z}, \quad \sqrt{\frac{x_1+x_2}{y_1+y_2}}

\alpha\beta\gamma\delta\epsilon\varepsilon\zeta\eta\theta\vartheta \kappa\lambda\mu\nu\xi\pi\rho\sigma\tau\upsilon \phi\varphi\chi\psi\omega

\beta^2,\quad \gamma_i,\quad \zeta_j,\quad \theta^*,\quad \kappa_\parallel,\quad \pi^2,\quad \sigma_{xy},\quad \tau^{-1},\quad \chi^\dagger,\quad \psi^\dagger,\quad \varpi_i,\quad \varkappa_j

\hat{x},\quad \hat{\alpha},\quad \bar{\alpha},\quad \tilde{\omega},\quad \dot{x},\quad \ddot{x},\quad \vec{k},\quad \widehat{xyz},\quad \widetilde{\alpha\beta}

A \leftarrow B,\quad A \rightarrow B,\quad A \longrightarrow B,\quad \boldsymbol{k} \mapsto \boldsymbol{k}+\boldsymbol{G},\quad \overleftarrow{AB},\quad \overrightarrow{AB},\quad \overleftrightarrow{AB}

H(\boldsymbol{k}) = \begin{pmatrix} \Delta & v(k_x - i k_y) \\ v(k_x + i k_y) & -\Delta \end{pmatrix}

\begin{bmatrix} a_{11} & a_{12} & a_{13} \\ a_{21} & a_{22} & a_{23} \\ a_{31} & a_{32} & a_{33} \end{bmatrix} \begin{bmatrix} x_1 \\ x_2 \\ x_3 \end{bmatrix} = \begin{bmatrix} b_1 \\ b_2 \\ b_3 \end{bmatrix}

f(x)= \begin{cases} x^2, & x \ge 0, \\ -x, & x < 0. \end{cases}

\begin{aligned} \nabla \cdot \boldsymbol{E} &= \frac{\rho}{\varepsilon_0}, \\ \nabla \cdot \boldsymbol{B} &= 0, \\ \nabla \times \boldsymbol{E} &= -\frac{\partial \boldsymbol{B}}{\partial t}, \\ \nabla \times \boldsymbol{B} &= \mu_0 \boldsymbol{J} + \mu_0\varepsilon_0\frac{\partial \boldsymbol{E}}{\partial t}. \end{aligned}