typo in 1.19 (fix issue#9)

Author: jeanwsr

chap1/chap1.tex

@@ -575,7 +575,7 @@ \subsubsection{The Variation Principle}
 \ex{1.19}
 \begin{equation}\label{key}
 \begin{aligned}
-\mathscr{E} &= \dfrac{\Braket{\tilde{\Phi} | -\dfrac{1}{2}\nabla^2 - \dfrac{1}{r} | \tilde{\Phi}}}{\Braket{\tilde{\Phi} | \tilde{\Phi}}} = \dfrac{N^2 \cdot 4\pi \intdinf r^2\dd r \e^{-\alpha r^2}\qty[-\dfrac{1}{2}(4 \alpha^2 r^2 - 6\alpha ) - \dfrac{1}{r}]\e^{-\alpha r^2}}{N^2\cdot 4\pi \intdinf r^2\dd r \e^{-2\alpha r^2}}\\
+\mathscr{E} &= \dfrac{\Braket{\tilde{\Phi} | -\dfrac{1}{2}\nabla^2 - \dfrac{1}{r} | \tilde{\Phi}}}{\Braket{\tilde{\Phi} | \tilde{\Phi}}} = \dfrac{N^2 \cdot 4\pi \intinf r^2\dd r \e^{-\alpha r^2}\qty[-\dfrac{1}{2}(4 \alpha^2 r^2 - 6\alpha ) - \dfrac{1}{r}]\e^{-\alpha r^2}}{N^2\cdot 4\pi \intinf r^2\dd r \e^{-2\alpha r^2}}\\
 &= \dfrac{-2\alpha^2\dfrac{24\pi^{1/2}}{64(2\alpha)^{5/2}} + 3\alpha\dfrac{2\pi^{1/2}}{8(2\alpha)^{3/2}} - \dfrac{1}{2(2\alpha)} }{\dfrac{2\pi^{1/2}}{8(2\alpha)^{3/2}}}\\
 &= -2\alpha^2\dfrac{12}{8(2\alpha)} + 3\alpha - \dfrac{2(2\alpha)^{1/2}}{\pi^{1/2} } \\
 &= \dfrac{3}{2}\alpha - \dfrac{2(2\alpha)^{1/2}}{\pi^{1/2} }