著者：W. Greiner，J. Reinhardt
出版：Springer-Verlag
p.I “J. Reinhart”→“J. Reinhardt”
p.7 “For times preceeding \(t_1\)”→“For times preceding \(t_1\)”
時間座標としての変数\(t\)と摂動の時刻\(t_1\)とが混同されており、“the scattered wave \(\Delta\psi(\boldsymbol x_1,t_1)\) is zero for \(t<t_1\)”などの不可解な表現が見られる。修正案はこのようになる。“\[\left(\mathrm i\hbar\frac{\partial}{\partial t_1}-\hat H_0\right)\psi(\boldsymbol x_1,t_1)=V(\boldsymbol x_1,t_1)\psi(\boldsymbol x_1,t_1)\ .\tag{1.10}\]As already mentioned, \(V(\boldsymbol x_1,t_1)\) acts only during the time interval \(\Delta t_1\). We
denote the resulting wave with the help of the free wave \(\phi\) as\[\psi(\boldsymbol x_1,t_1)=\phi(\boldsymbol x_1,t_1)+\Delta\psi(\boldsymbol x_1,t_1)\ ,\tag{1.11}\]where \(\phi\) solves the free Schrödinger equation\[\left(\mathrm i\hbar\frac{\partial}{\partial t_1}-\hat H_0\right)\phi(\boldsymbol x_1,t_1)=0\tag{1.12}\]and where the scattered wave \(\Delta\psi(\boldsymbol x_1,t_1)\) is zero for \(t<t_1\). Inserting (1.11) into
(1.10) and taking into account (1.12), we find\[\left(\mathrm i\hbar\frac{\partial}{\partial t_1}-\hat H_0\right)\Delta\psi(\boldsymbol x_1,t_1)=V(\boldsymbol x_1,t_1)(\phi(\boldsymbol x_1,t_1)+\Delta\psi(\boldsymbol x_1,t_1))\tag{1.13}\]and, neglecting the small term \(V\Delta\psi\) on the right-hand side,\[\left(\mathrm i\hbar\frac{\partial}{\partial t_1}-\hat H_0\right)\Delta\psi(\boldsymbol x_1,t_1)=V(\boldsymbol x_1,t_1)\phi(\boldsymbol x_1,t_1)\ .\tag{1.14}\]”→“\[\left(\mathrm i\hbar\frac{\partial}{\partial t}-\hat H_0\right)\psi(\boldsymbol x_1,t)=V(\boldsymbol x_1,t)\psi(\boldsymbol x_1,t)\ .\tag{1.10}\]As already mentioned, \(V(\boldsymbol x_1,t)\) acts only during the time interval \(t_1\) to
\(t_1+\Delta t_1\). We denote the resulting wave with the help of the free wave \(\phi\) as\[\psi(\boldsymbol x_1,t)=\phi(\boldsymbol x_1,t)+\Delta\psi(\boldsymbol x_1,t)\ ,\tag{1.11}\]where \(\phi\) solves the free Schrödinger equation\[\left(\mathrm i\hbar\frac{\partial}{\partial t}-\hat H_0\right)\phi(\boldsymbol x_1,t)=0\tag{1.12}\]and where the scattered wave \(\Delta\psi(\boldsymbol x_1,t)\) is zero for \(t<t_1\). Inserting (1.11) into
(1.10) and taking into account (1.12), we find\[\left(\mathrm i\hbar\frac{\partial}{\partial t}-\hat H_0\right)\Delta\psi(\boldsymbol x_1,t)=V(\boldsymbol x_1,t)(\phi(\boldsymbol x_1,t)+\Delta\psi(\boldsymbol x_1,t))\tag{1.13}\]and, neglecting the small term \(V\Delta\psi\) on the right-hand side,\[\left(\mathrm i\hbar\frac{\partial}{\partial t}-\hat H_0\right)\Delta\psi(\boldsymbol x_1,t)=V(\boldsymbol x_1,t)\phi(\boldsymbol x_1,t)\ .\tag{1.14}\]”
p.8 l.15 “\(G_0(\boldsymbol x',t';\boldsymbol x,t)\)”→“\(G_0(\boldsymbol x',t';\boldsymbol{x}_1,t_1)\)”
(1.18) “\(\begin{align}=&\mathrm{i}\int\mathrm{d}^3x\bigl(G_0(\boldsymbol x',t';\boldsymbol x,t)\\&+\int\mathrm d^3x_1\Delta t_1G_0(\boldsymbol x',t';\boldsymbol x_1,t_1)\frac{1}{\hbar}V(\boldsymbol x_1,t_1)G_0(\boldsymbol x_1,t_1;\boldsymbol x,t)\bigr)\phi(\boldsymbol x,t)\ .\end{align}\)”→“\(\begin{align}=&\mathrm{i}\int\mathrm{d}^3x\left(G_0(\boldsymbol x',t';\boldsymbol x,t)\phantom{\int}\right.\\&+\left.\int\mathrm d^3x_1\Delta t_1G_0(\boldsymbol x',t';\boldsymbol x_1,t_1)\frac{1}{\hbar}V(\boldsymbol x_1,t_1)G_0(\boldsymbol x_1,t_1;\boldsymbol x,t)\right)\phi(\boldsymbol x,t)\ .\end{align}\)”
p.9 Fig. 1.3b “\((\boldsymbol x_1,t)\)”→“\((\boldsymbol x_1,t_1)\)”
l.12 “\(\psi(2)\)”→“\(\psi(x_2)\)”
p.10 l.21 “\(G(x',x)\)”→“\(G(x';x)\)”
p.12 (1.31) “\(G_0^+(x',x_1)\)”→“\(G_0^+(x';x_1)\)”（3ヶ所）
p.16 (1) “\(G^-(x_1,x)\)”→“\(G^-(x_1;x)\)”
p.17 (5) “\(t\to-\infty\)”→“\(t''\to-\infty\)”
p.21 “\(\hat S\hat S{}^+\)”→“\(\hat S\hat S{}^\dagger\)”
“\(\mbox{1}\hspace{-0.25em}\mbox{l}=|\gamma\rangle\langle\gamma|\)”→“\(\displaystyle\mbox{1}\hspace{-0.25em}\mbox{l}=\sum_\gamma|\gamma\rangle\langle\gamma|\)”
“\(\left\langle\gamma\mathrel{}\middle|\hat S{}^+\middle|\mathrel{}\alpha\right\rangle\)”→“\(\left\langle\gamma\mathrel{}\middle|\hat S{}^\dagger\middle|\mathrel{}\alpha\right\rangle\)”
p.23 (1.52) “\(\left\langle\beta\mathrel{}\middle|\hat S\middle|\mathrel{}\alpha\right\rangle=\)”→“\(\left\langle\beta'\mathrel{}\middle|\hat S\middle|\mathrel{}\alpha'\right\rangle=\)”
p.28 (1.71) “\(\boldsymbol p(\boldsymbol x'-\boldsymbol x)\)”→“\(\boldsymbol p\cdot(\boldsymbol x'-\boldsymbol x)\)”（2ヶ所）
p.29 (1.74) “\(\mathrm d^3\boldsymbol p\)”→“\(\mathrm d^3p\)”（2ヶ所）
p.31 “The iteration of (1.82)”→“The iteration of (1.83)”
p.34 (17) “\(\displaystyle\mathop{\int}_{-\infty}^\infty\mathrm dp_x\exp\left(-\frac{\tau\xi^2}{a^2}-\frac{a^2R_x^2}{4\tau}\right)\ \mathrm dp_x\)”→“\(\displaystyle\mathop{\int}_{-\infty}^\infty\mathrm dp_x\exp\left(-\frac{\tau\xi^2}{a^2}-\frac{a^2R_x^2}{4\tau}\right)\)”
p.37 (18) “\(\boldsymbol\nabla\varPsi\)”→“\(\boldsymbol{\nabla}^2\varPsi\)”
(19) “\(\mathrm d^3\boldsymbol x'\)”→“\(\mathrm d^3x'\)”
p.89 (3.25) “\(\displaystyle\frac{\mathrm{d}\bar{\sigma}}{\mathrm{d}\varOmega}\)”→“\(\displaystyle\frac{\mathrm{d}\bar{\sigma}}{\mathrm{d}\varOmega_f}\)”
p.101 (4) “\(\displaystyle\frac{\mathrm{d}\bar{\sigma}_{e^+}}{\mathrm{d}\varOmega}\)”→“\(\displaystyle\frac{\mathrm{d}\bar{\sigma}_{e^+}}{\mathrm{d}\varOmega_f}\)”
(10) 同上。
p.102 l.1 “(3.31)”→“(3.35)”
l.14 “irrevelant”→“irrelevant”
p.118 (3.103) “\(\displaystyle=\frac{e^2e_\mathrm{p}^2(4\pi)^2}{2m_0^2M_0^2(q^2)^2}\Bigl\{2M_0^2EE'-p_f\cdot p_i\left[M_0^2+M_0(E'-E)\right]+m_0^2M_0^2\Bigr\}\)”→“\(\displaystyle=\frac{e^2e_\mathrm{p}^2(4\pi)^2}{2m_0^2M_0^2(q^2)^2}\Bigl\{2M_0^2EE'-p_f\cdot p_i\left[M_0^2+M_0(E'-E)\right]+m_0^2M_0^2+2M_0(E'-E)m_0^2\Bigr\}\)”
p.119 l.1 “(3.101)”→“(3.102)”
(3.106) “\(\displaystyle\frac{m_0}{E}\ll1\)”→“for \(\displaystyle\frac{m_0}{E},\frac{m_0}{E'}\ll1\)”
p.122 l.9 “bilinear convariants”→“bilinear covariants”
l.13 “\(\sigma_{\nu\mu}=(\mathrm{i}/2)(\gamma_\mu\gamma_\nu-\gamma_\nu\gamma_\mu)\)”→“\(\sigma_{\mu\nu}=(\mathrm{i}/2)(\gamma_\mu\gamma_\nu-\gamma_\nu\gamma_\mu)\)”
p.123 (9) “\(\displaystyle W=e_\mathrm{p}\int\mathrm{d}^3x\ A^\mu(\boldsymbol{x})J_\mu(\boldsymbol{x})\)”→“\(\displaystyle W=\int\mathrm{d}^3x\ A^\mu(\boldsymbol{x})J_\mu(\boldsymbol{x})\)”
p.124 (17) “\(\displaystyle(\bar{u}\boldsymbol{\varSigma}u)\frac{1}{V}\int\mathrm{d}^3x\ \mathrm{e}^{-\mathrm{i}\boldsymbol{q}\cdot\boldsymbol{x}}\,\nabla\times\boldsymbol{A}(\boldsymbol{x})\)”→“\(\displaystyle(\bar{u}\boldsymbol{\varSigma}u)\cdot\frac{1}{V}\int\mathrm{d}^3x\ \mathrm{e}^{-\mathrm{i}\boldsymbol{q}\cdot\boldsymbol{x}}\,\nabla\times\boldsymbol{A}(\boldsymbol{x})\)”
(18) “\(F_1^n\)”→“\(F_1^\mathrm{n}\)”
“\(F_2^n\)”→“\(F_2^\mathrm{n}\)”
l.26 “simplifies”→“is simplified”
pp.124f. “The squared spin-averaged transition matrix element”→“The spin-averaged squared invariant amplitude” “transition matrix”（T行列、遷移行列）は本文中の他の箇所に見当たらない。
p.127 l.1 “(23)”→“(25)”
(30) “\(\frac{q^2}{2M_0}\)”→“\(\frac{q^2}{2M_0^2}\)”
p.128 (33) “\(\left(\frac{\mathrm{d}\bar\sigma}{\mathrm{d}\varOmega}\right)_\mathrm{Mott}\)”が具体的に述べられていないため確かなことは判らないが、仮にこれがp.92 (3.39)において\(Z=1,\beta\to1\)とした\(\left(\frac{\mathrm{d}\bar\sigma}{\mathrm{d}\varOmega}\right)_\mathrm{Mott}=\frac{e^2e_\mathrm{p}^2}{4E^2\sin^2\frac{\theta}{2}}\cos^2\frac{\theta}{2}\)というものならば、式(33)は次のように修正されるべきである。“\(\displaystyle\frac{\mathrm{d}\bar\sigma}{\mathrm{d}\varOmega}=\left(\frac{\mathrm{d}\bar\sigma}{\mathrm{d}\varOmega}\right)_\mathrm{Mott}\left[\frac{G_\mathrm{E}^2(q^2)+\tau G_\mathrm{M}^2(q^2)}{1+\tau}+2\tau G_\mathrm{M}^2(q^2)\tan^2\frac{\theta}{2}\right]\)”→“\(\begin{align}\frac{\mathrm{d}\bar\sigma}{\mathrm{d}\varOmega}=&\left(\frac{\mathrm{d}\bar\sigma}{\mathrm{d}\varOmega}\right)_\mathrm{Mott}\left(1+\frac{2E}{M_0}\sin^2\frac{\theta}{2}\right)^{-1}\\&\times\left[\frac{G_\mathrm{E}^2(q^2)+\tau G_\mathrm{M}^2(q^2)}{1+\tau}+2\tau G_\mathrm{M}^2(q^2)\tan^2\frac{\theta}{2}\right]\end{align}\)”
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