1.麦克斯韦方程组\Large\mathcal{Maxwell's\ \ equations}\\ \begin{split} &\oint_S\bm{D}\cdot{\rm d}\bm{S}=q\\ &\oint_S\bm{B}\cdot{\rm d}\bm{S}=0\\ &\oint_l\bm{E}\cdot{\rm d}\bm{l}=-\int_S\frac{\partial \bm{B}}{\partial t}\cdot{\rm d}\bm{S}\\ &\oint_l\bm{H}\cdot{\rm d}\bm{l}=\int_S\left(\bm{j_{\rm c}}+\frac{\partial\bm{D}}{\partial t}\right)\cdot{\rm d}\bm{S} \end{split}\Large\mathcal{Maxwell's\ \ equations}\\ \begin{split} &\oint_S\bm{D}\cdot{\rm d}\bm{S}=q\\ &\oint_S\bm{B}\cdot{\rm d}\bm{S}=0\\ &\oint_l\bm{E}\cdot{\rm d}\bm{l}=-\int_S\frac{\partial \bm{B}}{\partial t}\cdot{\rm d}\bm{S}\\ &\oint_l\bm{H}\cdot{\rm d}\bm{l}=\int_S\left(\bm{j_{\rm c}}+\frac{\partial\bm{D}}{\partial t}\right)\cdot{\rm d}\bm{S} \end{split}

2.麦克斯韦关系式

\Large\mathcal{Maxwell\ \ relations}\\ \begin{split} {\rm d}U=\begin{vmatrix}\color{red}{T}&\color{blue}{p}\\\color{red}{{\rm d}V}&\color{blue}{{\rm d}S}\end{vmatrix}=T{\rm d}S-p{\rm d}V&\\ \left(\color{red}{\frac{\partial T}{\partial V}}\right)_S+\left(\color{blue}{\frac{\partial p}{\partial S}}\right)_V=0\\ {\rm d}H=\begin{vmatrix}\color{red}{T}&-\color{blue}{V}\\\color{red}{{\rm d}p}&\color{blue}{{\rm d}S}\end{vmatrix}=T{\rm d}S+V{\rm d}p&\\ \left(\color{red}{\frac{\partial T}{\partial p}}\right)_S-\left(\color{blue}{\frac{\partial V}{\partial S}}\right)_p=0\\ {\rm d}A=\begin{vmatrix}-\color{red}{S}&\color{blue}{p}\\\color{red}{{\rm d}V}&\color{blue}{{\rm d}T}\end{vmatrix}=-S{\rm d}T-p{\rm d}V&\\ -\left(\color{red}{\frac{\partial S}{\partial V}}\right)_T+\left(\color{blue}{\frac{\partial p}{\partial T}}\right)_V=0\\ {\rm d}G=\begin{vmatrix}-\color{red}{S}&-\color{blue}{V}\\\color{red}{{\rm d}p}&\color{blue}{{\rm d}T}\end{vmatrix}=-S{\rm d}T+V{\rm d}p&\\ -\left(\color{red}{\frac{\partial S}{\partial p}}\right)_T-\left(\color{blue}{\frac{\partial V}{\partial T}}\right)_p=0\\ \end{split}\Large\mathcal{Maxwell\ \ relations}\\ \begin{split} {\rm d}U=\begin{vmatrix}\color{red}{T}&\color{blue}{p}\\\color{red}{{\rm d}V}&\color{blue}{{\rm d}S}\end{vmatrix}=T{\rm d}S-p{\rm d}V&\\ \left(\color{red}{\frac{\partial T}{\partial V}}\right)_S+\left(\color{blue}{\frac{\partial p}{\partial S}}\right)_V=0\\ {\rm d}H=\begin{vmatrix}\color{red}{T}&-\color{blue}{V}\\\color{red}{{\rm d}p}&\color{blue}{{\rm d}S}\end{vmatrix}=T{\rm d}S+V{\rm d}p&\\ \left(\color{red}{\frac{\partial T}{\partial p}}\right)_S-\left(\color{blue}{\frac{\partial V}{\partial S}}\right)_p=0\\ {\rm d}A=\begin{vmatrix}-\color{red}{S}&\color{blue}{p}\\\color{red}{{\rm d}V}&\color{blue}{{\rm d}T}\end{vmatrix}=-S{\rm d}T-p{\rm d}V&\\ -\left(\color{red}{\frac{\partial S}{\partial V}}\right)_T+\left(\color{blue}{\frac{\partial p}{\partial T}}\right)_V=0\\ {\rm d}G=\begin{vmatrix}-\color{red}{S}&-\color{blue}{V}\\\color{red}{{\rm d}p}&\color{blue}{{\rm d}T}\end{vmatrix}=-S{\rm d}T+V{\rm d}p&\\ -\left(\color{red}{\frac{\partial S}{\partial p}}\right)_T-\left(\color{blue}{\frac{\partial V}{\partial T}}\right)_p=0\\ \end{split}

3.洛伦兹变换式

\Large\mathcal{Lorentz\ \ transformation\ equations}\\ \begin{cases} x'=\frac{x-vt}{\sqrt{1-\frac{v^2}{c^2}}}\\ y'=y\\ z'=z\\ t'=\frac{t-\frac{vx}{c^2}}{\sqrt{1-\frac{v^2}{c^2}}} \end{cases}\Large\mathcal{Lorentz\ \ transformation\ equations}\\ \begin{cases} x'=\frac{x-vt}{\sqrt{1-\frac{v^2}{c^2}}}\\ y'=y\\ z'=z\\ t'=\frac{t-\frac{vx}{c^2}}{\sqrt{1-\frac{v^2}{c^2}}} \end{cases}

4.质能方程

\Large\mathcal{Mass-energy\ \ equivalence\ \ equation}\\ E=mc^2\Large\mathcal{Mass-energy\ \ equivalence\ \ equation}\\ E=mc^2

5.薛定谔方程

\Large\mathcal{Schr\ddot{o}dinger\ \ equation}\\ \left(-\frac{h^2}{8\pi^2m}\nabla^2+\hat{V}\right)\psi=E\psi\Large\mathcal{Schr\ddot{o}dinger\ \ equation}\\ \left(-\frac{h^2}{8\pi^2m}\nabla^2+\hat{V}\right)\psi=E\psi

etc.