身につくシュレーディンガー方程式（牟田淳著、技術評論社）
初版第1刷正誤表（第2刷修正済み）
初版1刷の正誤表です。第2刷では修正されています。他に間違い等ございましたら「お問い合わせ」よりご連絡ください。（2021年2月22日）
- 138ページ式（6.75）符号が逆
（誤）$+ \cos \frac{(n+m) \pi}{a} x$ $\Longrightarrow$ （正）$- \cos \frac{(n+m) \pi}{a} x$
- 169ページ図7.12 「マイナス（$-$）不要」
（誤）$-\frac{1}{2}m\omega^2 x^2$ $\Longrightarrow $ （正） $ \frac{1}{2}m\omega^2 x^2$
- 208ページ 具体的なラプラシアンの計算
異なる変数による$\varphi$の2階偏微分の項が抜け落ちていました（抜け落ちていた項は計算すると全てキャンセルして消えるのですが。。）- 式(9.20)6行目から、赤字部分を追加 \begin{eqnarray} & &= [ \sin \theta \cos \phi \frac{\partial^2 \varphi}{\partial r^2} + \cos \theta \cos \phi\ ( -\frac{1}{r^2}\frac{\partial
\varphi}{\partial \theta} \textcolor{red}{+\frac{1}{r}\frac{\partial^2 \varphi}{\partial \theta \partial r}} ) \nonumber \\ & & -\frac{\sin \phi}{\sin \theta} ( -\frac{1}{r^2}
\frac{\partial \varphi}{\partial \phi} \textcolor{red}{+\frac{1}{r}\frac{\partial^2 \varphi}{\partial\phi \partial r}} ) ] \sin \theta \cos \phi \nonumber \\ & & +[ \cos\phi (\cos
\theta \frac{\partial \varphi}{\partial r} \textcolor{red}{+\sin \theta \frac{\partial^2 \varphi}{\partial r \partial \theta} }) + \frac{1}{r} \cos \phi (-\sin \theta \frac{\partial
\varphi}{\partial \theta} \textcolor{red}{+\cos \theta \frac{\partial^2 \varphi}{\partial^2 \theta}} ) \nonumber \\ & & -\frac{1}{r}\sin \phi ( - \frac{\cos \theta}{\sin^2 \theta}
\frac{\partial \varphi}{\partial \phi} \textcolor{red}{+\frac{1}{\sin \theta} \frac{\partial^2 \varphi}{\partial \phi \partial \theta} } ) ] \frac{\cos \theta \cos \phi}{r} \nonumber \\
& & +[-\sin \theta (-\sin \phi \frac{\partial \varphi}{\partial r} \textcolor{red}{+\cos \phi \frac{\partial^2 \varphi}{\partial r \partial \phi} } ) -\frac{1}{r}\cos \theta
(-\sin \phi \frac{\partial \varphi}{\partial \theta} \textcolor{red}{+\cos \phi\frac{\partial^2 \varphi}{\partial \theta \partial \phi} } ) \nonumber \\ & &
+\frac{1}{r}\frac{1}{\sin \theta} ( \cos \phi \frac{\partial \varphi}{\partial \phi} + \sin \phi \frac{\partial^2 \varphi}{\partial \phi^2} ) ] \frac{\sin \phi}{r \sin \theta} \nonumber
\end{eqnarray}
- 式(9.20)最後の行に以下の行を追加 \begin{eqnarray} & & +\frac{2}{r} [ \cos \theta \sin \theta \cos^2 \phi \frac{\partial^2 \varphi}{\partial r \partial \theta} -\sin \phi \cos \phi
\frac{\partial^2 \varphi}{\partial r \partial\phi} -\frac{1}{r}\frac{\cos \theta }{\sin \theta}\sin \phi \cos \phi \frac{\partial^2 \varphi}{\partial \theta \partial \phi} ] \nonumber
\end{eqnarray}
- 式(9.21)6行目から、赤字部分を追加 \begin{eqnarray} & &= [ \sin \theta \sin \phi \frac{\partial^2 \varphi}{\partial r^2} + \cos \theta \sin \phi\ ( -\frac{1}{r^2}\frac{\partial
\varphi}{\partial \theta} \textcolor{red}{+\frac{1}{r}\frac{\partial^2 \varphi}{\partial \theta \partial r}} ) \nonumber \\ & & +\frac{\cos \phi}{\sin \theta} ( -\frac{1}{r^2}
\frac{\partial \varphi}{\partial \phi} \textcolor{red}{+\frac{1}{r}\frac{\partial^2 \varphi}{\partial\phi \partial r}} ) ] \sin \theta \sin \phi \nonumber \\ & & +[ \sin\phi (\cos
\theta \frac{\partial \varphi}{\partial r} \textcolor{red}{+\sin \theta \frac{\partial^2 \varphi}{\partial r \partial \theta} }) + \frac{1}{r} \sin \phi (-\sin \theta \frac{\partial
\varphi}{\partial \theta} \textcolor{red}{+\cos \theta \frac{\partial^2 \varphi}{\partial^2 \theta}} ) \nonumber \\ & & +\frac{1}{r}\cos \phi ( - \frac{\cos \theta}{\sin^2 \theta}
\frac{\partial \varphi}{\partial \phi} \textcolor{red}{+\frac{1}{\sin \theta} \frac{\partial^2 \varphi}{\partial \phi \partial \theta} } ) ] \frac{\cos \theta \sin \phi}{r} \nonumber \\
& & +[\sin \theta (\cos \phi \frac{\partial \varphi}{\partial r} \textcolor{red}{+\sin \phi \frac{\partial^2 \varphi}{\partial r \partial \phi} } ) +\frac{1}{r}\cos \theta (\cos
\phi \frac{\partial \varphi}{\partial \theta} \textcolor{red}{+\sin \phi\frac{\partial^2 \varphi}{\partial \theta \partial \phi} } ) \nonumber \\ & & +\frac{1}{r}\frac{1}{\sin
\theta} ( -\sin \phi \frac{\partial \varphi}{\partial \phi} + \cos \phi \frac{\partial^2 \varphi}{\partial \phi^2} ) ] \frac{\cos \phi}{r \sin \theta} \nonumber \end{eqnarray}
- 式(9.21)最後の行に以下の行を追加 \begin{eqnarray} & & +\frac{2}{r} [ \cos \theta \sin \theta \sin^2 \phi \frac{\partial^2 \varphi}{\partial r \partial \theta} +\sin \phi \cos \phi
\frac{\partial^2 \varphi}{\partial r \partial\phi} +\frac{1}{r}\frac{\cos \theta }{\sin \theta}\sin \phi \cos \phi \frac{\partial^2 \varphi}{\partial \theta \partial \phi} ] \nonumber
\end{eqnarray}
- 式(9.22)4行目から、赤字部分を追加 \begin{eqnarray} & & [\cos \theta \frac{\partial^2 \varphi}{\partial r^2}-\sin \theta (-\frac{1}{r^2}\frac{\partial\varphi}{\partial \theta}
\textcolor{red}{+\frac{1}{r}\frac{\partial^2 \varphi}{\partial \theta \partial r} } ) ] \cos \theta \nonumber \\ & & +[(\sin \theta \frac{\partial \varphi}{\partial r}
\textcolor{red}{- \cos \theta \frac{\partial^2 \varphi}{\partial r \partial \theta}}) +\frac{1}{r}(\cos \theta \frac{\partial \varphi}{\partial \theta} + \sin \theta \frac{\partial^2
\varphi}{\partial \theta^2}]\frac{\sin \theta}{r} \nonumber \\ &=& \cos^2 \theta \frac{\partial^2 \varphi}{\partial r^2} + \sin^2 \theta \frac{1}{r} \frac{\partial
\varphi}{\partial r} +\frac{1}{r^2}[ 2 \sin \theta \cos \theta \frac{\partial \varphi}{\partial \theta} + \sin^2 \theta \frac{\partial^2 \varphi}{\partial\theta^2}] \nonumber \\ &
& \textcolor{red}{-\frac{2}{r}\cos \theta \sin \theta \frac{\partial^2 \varphi}{\partial r \partial \theta}} \nonumber \end{eqnarray}
- 式(9.23)下から２行目に以下の項を追加（全てキャンセルして0になる） \begin{eqnarray} & & +\frac{2}{r}[(\cos \theta \sin \theta \cos \phi^2 + \cos \theta \sin \theta \sin \phi^2- \cos \theta \sin
\theta)\frac{\partial^2 \varphi}{\partial r \partial \theta} \nonumber \\ & & +(-\sin \phi \cos \phi+\sin \phi \cos \phi) \frac{\partial^2 \varphi}{\partial r \partial \phi}
\nonumber \\ & & +(-\frac{1}{r}\frac{\cos \theta}{\sin \theta}\sin \phi \cos \phi +\frac{1}{r}\frac{\cos \theta}{\sin \theta}\sin \phi \cos \phi) \frac{\partial^2
\varphi}{\partial \theta \partial \phi}] \nonumber \end{eqnarray}
- 式(9.20)6行目から、赤字部分を追加 \begin{eqnarray} & &= [ \sin \theta \cos \phi \frac{\partial^2 \varphi}{\partial r^2} + \cos \theta \cos \phi\ ( -\frac{1}{r^2}\frac{\partial
\varphi}{\partial \theta} \textcolor{red}{+\frac{1}{r}\frac{\partial^2 \varphi}{\partial \theta \partial r}} ) \nonumber \\ & & -\frac{\sin \phi}{\sin \theta} ( -\frac{1}{r^2}
\frac{\partial \varphi}{\partial \phi} \textcolor{red}{+\frac{1}{r}\frac{\partial^2 \varphi}{\partial\phi \partial r}} ) ] \sin \theta \cos \phi \nonumber \\ & & +[ \cos\phi (\cos
\theta \frac{\partial \varphi}{\partial r} \textcolor{red}{+\sin \theta \frac{\partial^2 \varphi}{\partial r \partial \theta} }) + \frac{1}{r} \cos \phi (-\sin \theta \frac{\partial
\varphi}{\partial \theta} \textcolor{red}{+\cos \theta \frac{\partial^2 \varphi}{\partial^2 \theta}} ) \nonumber \\ & & -\frac{1}{r}\sin \phi ( - \frac{\cos \theta}{\sin^2 \theta}
\frac{\partial \varphi}{\partial \phi} \textcolor{red}{+\frac{1}{\sin \theta} \frac{\partial^2 \varphi}{\partial \phi \partial \theta} } ) ] \frac{\cos \theta \cos \phi}{r} \nonumber \\
& & +[-\sin \theta (-\sin \phi \frac{\partial \varphi}{\partial r} \textcolor{red}{+\cos \phi \frac{\partial^2 \varphi}{\partial r \partial \phi} } ) -\frac{1}{r}\cos \theta
(-\sin \phi \frac{\partial \varphi}{\partial \theta} \textcolor{red}{+\cos \phi\frac{\partial^2 \varphi}{\partial \theta \partial \phi} } ) \nonumber \\ & &
+\frac{1}{r}\frac{1}{\sin \theta} ( \cos \phi \frac{\partial \varphi}{\partial \phi} + \sin \phi \frac{\partial^2 \varphi}{\partial \phi^2} ) ] \frac{\sin \phi}{r \sin \theta} \nonumber
\end{eqnarray}