薛定谔
从经典力学和几何光学间的类比，提出了波动光学的波动力学方程
1. 含时薛定谔方程（核心）： \[ i\hbar \frac{\partial}{\partial t} \Psi(\mathbf{r},t) = \hat{H} \Psi(\mathbf{r},t) \]
3. 薛定谔方程的经典对应形式：\[ i\hbar \frac{\partial \Psi}{\partial t} = \left( -\frac{\hbar^2}{2m} \nabla^2 + V(\mathbf{r},t) \right) \Psi \]
5. 动量算符的薛定谔表示：\[ \hat{\mathbf{p}} = -i\hbar \nabla = -i\hbar \left( \frac{\partial}{\partial x}\mathbf{i} + \frac{\partial}{\partial y}\mathbf{j} + \frac{\partial}{\partial z}\mathbf{k} \right) \]
7. 概率流密度连续性方程：\[ \frac{\partial \rho}{\partial t} + \nabla \cdot \mathbf{j} = 0,\ \rho=|\Psi|^2,\ \mathbf{j}=-\frac{i\hbar}{2m}(\Psi^*\nabla\Psi - \Psi\nabla\Psi^*) \]
9. 多粒子系统薛定谔方程：\[ i\hbar \frac{\partial}{\partial t} \Psi(\mathbf{r}_1,\mathbf{r}_2,...,\mathbf{r}_N,t) = \left( \sum_{i=1}^N \hat{H}_i + \sum_{i
......
提出薛定谔猫思想实验，证明量子力学在宏观条件下的不完备性
2. 定态薛定谔方程：\[ \hat{H} \psi(\mathbf{r}) = E \psi(\mathbf{r}) \]
4. 波函数归一化条件：\[ \int_{-\infty}^{\infty} |\Psi(\mathbf{r},t)|^2 d^3\mathbf{r} = 1 \]
6. 薛定谔猫态（量子叠加态）：\[ |\Psi\rangle = \frac{1}{\sqrt{2}} (|\text{活猫}\rangle + |\text{死猫}\rangle) \]
8. 角动量算符对易关系：\[ [\hat{L}_x, \hat{L}_y] = i\hbar \hat{L}_z,\ [\hat{L}^2, \hat{L}_i] = 0 \ (i=x,y,z) \]
10. 薛定谔量子配分函数：\[ Z = \sum_n e^{-E_n/(k_B T)} = \text{Tr}(e^{-\hat{H}/(k_B T)}) \]