https://haifei-home.pages.dev/tags/%E6%95%B0%E5%AD%A6%E7%89%A9%E7%90%86%E6%96%B9%E6%B3%95/Recent content in 数学物理方法 on Haifei's HomeHugozh-CNhfwang132@gmail.com (hfwang132)hfwang132@gmail.com (hfwang132)This work is licensed under a Creative Commons Attribution-NonCommercial 4.0 International License.Wed, 01 May 2024 03:04:30 +0800https://haifei-home.pages.dev/post_20240501_%E4%BA%A7%E7%94%9F%E6%B9%AE%E7%81%AD%E7%AE%97%E7%AC%A6%E6%98%AF%E6%80%8E%E4%B9%88%E5%BE%97%E5%88%B0%E7%9A%84/Wed, 01 May 2024 03:04:30 +0800hfwang132@gmail.com (hfwang132)https://haifei-home.pages.dev/post_20240501_%E4%BA%A7%E7%94%9F%E6%B9%AE%E7%81%AD%E7%AE%97%E7%AC%A6%E6%98%AF%E6%80%8E%E4%B9%88%E5%BE%97%E5%88%B0%E7%9A%84/<p>产生湮灭算符的定义动机很简单，完全可以从经典力学中得到。</p> <p>想想我们是怎么解经典谐振子的。由于位置和动量是耦合起来的：</p> <p>$\begin{cases} \frac{\mathrm{d}x}{\mathrm{d}t} = \omega p \\ \frac{\mathrm{d}p}{\mathrm{d}t} = -\omega x \end{cases}$</p> <p>即</p> <p>$\frac{\mathrm{d}}{\mathrm{d}t} \begin{bmatrix} x \\ p \end{bmatrix} = \begin{bmatrix} 0 &amp; \omega \\ -\omega &amp; 0 \end{bmatrix} \begin{bmatrix} x \\ p \end{bmatrix}$</p>