\[ \newcommand{dn}[3]{\frac{\mathrm{d}^{#3} #1}{\mathrm{d} #2^{#3}}}
\newcommand{\d}[2]{\frac{\mathrm{d} #1}{\mathrm{d} #2}}
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\newcommand{\ddd}[2]{\frac{\mathrm{d}^3 #1}{\mathrm{d} {#2}^3}}
\newcommand{\pdn}[3]{\frac{\partial^{#3} #1}{\partial {#2}^{#3}}}
\newcommand{\pd}[2]{\frac{\partial #1}{\partial #2}}
\newcommand{\pdd}[2]{\frac{\partial^2 #1}{\partial {#2}^2}}
\newcommand{\pddd}[2]{\frac{\partial^3 #1}{\partial {#2}^3}}
\newcommand{\p}{\partial}
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\newcommand{\Re}{\mathrm{Re}}
\newcommand{\Im}{\mathrm{Im}}
\newcommand{\bra}[1]{\left\langle #1 \right|}
\newcommand{\ket}[1]{\left|#1 \right\rangle}
\newcommand{\braket}[2]{\left\langle #1 \middle|#2 \right\rangle}
\newcommand{\inner}[2]{\left\langle #1 ,#2 \right\rangle}
\newcommand{\l}{\left} \newcommand{\m}{\middle} \newcommand{\r}{\right}
\newcommand{\f}[2]{\frac{#1}{#2}} \newcommand{\eps}{\varepsilon}
\newcommand{\ra}{\rightarrow} \newcommand{\F}{\mathcal{F}}
\newcommand{\L}{\mathcal{L}} \newcommand{\t}{\quad}
\newcommand{\intinf}{\int_{-\infty}^{+\infty}}
\newcommand{\R}{\mathcal{R}} \newcommand{\C}{\mathcal{C}}
\newcommand{\Z}{\mathcal{Z}} \newcommand{\bm}[1]{\boldsymbol{#1}} \]
ラグランジュの力学
ラグランジュの運動方程式
\[
\d{}{t}\pd{L}{\dot{q}_i}-\pd{L}{q_i}=f_i
\]
ハミルトンの力学
一般化運動量
\[
p_i := \pd{L}{\dot{q}_i}
\]
ハミルトニアン
\[
H(q_i,p_i,t) := p_iq_i - L
\]
ハミルトンの運動方程式
\[
\dot{q_i}=\pd{H}{p_i}, \quad \dot{p_i} = -\pd{H}{q_i}
\]
電磁気の正準方程式
量子化
