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## Believed to be typos in Desai’s QM Text

Posted by peeterjoot on November 25, 2011

[Click here for a PDF of this post with nicer formatting and figures if the post had any (especially if my latex to wordpress script has left FORMULA DOES NOT PARSE errors.)]

Here’s a few more typos, in addition to those noted previously, spotted in our QM text [1] from chapters we’ve covered in this term’s class.

# Chapter 17.

\begin{itemize}
\item Page 297. (17.38). appears to be off by a factor of $2$ since $(\sin^2 2x)' = 2 \sin x \cos x = \sin(2 x)$.
\item Page 311. (17.134). $d/dt'$ missing on the $H_{ss}'$ term in the integral.
\item Page 311. (17.136). First term (non-integral part) should be negated.
\item Page 312. (17.144). Sign on $\lambda$ before sum positive instead of negative.
\item Page 313. (17.149). $1/\hbar$ missing.
\item Page 313. (17.152,17.154). extra bra around the bra.
\item Page 313. (17.153). bra missing on $\phi_n$
\end{itemize}

# Chapter 24.

\begin{itemize}
\item Page 450. (24.6). $k^2(x)$ should be $k^2(x) u$.
\item Page 452. (24.18). In the $E < V$ case should be $1/\sqrt{\kappa}$ instead of $1/\sqrt{k}$ (although what's in the text is strictly still correct since it only changes the phase of the wavefunction).

\item Page 455. (24.40). RHD should be multiplied by $\hbar$.

\item Page 460. (24.71). $\psi$ should be $\phi$.
\item Page 460. Third paragraph. $(\mathbf{r}_1 - \mathbf{r})$ should be $(\mathbf{r}_1 - \mathbf{r}_2)$.
\item Page 460. (24.76). The integral should be $1/3$, not $5 \pi/32$. This messes up some of the subsequent stuff, unless there is also another compensating error. Note that one can check this easily since the derivative of $-1/(3 (1+x)^3)$ is $(1 + x)^{-4}$.
\end{itemize}

# Chapter 25.

\begin{itemize}
\item Page 471. (25.18). $i$ subscripts missing on $\mathcal{L}$ and $\dot{y}^2$.
\end{itemize}

# Chapter 26.

\begin{itemize}
\item Page 486. (26.60). $\mathbf{n} \times \mathbf{r} \cdot \boldsymbol{\nabla}$ ought to have braces and read $(\mathbf{n} \times \mathbf{r}) \cdot \boldsymbol{\nabla}$.
\item Page 487. (26.67). $0$ in the $3,3$ position should be $1$.
\item Page 489. before (26.84). For rotations about the imaginary axis was probably meant to be the i’th axis.
\item Page 495. (26.149,26.150). Looks like $\hbar$‘s are missing (esp. compared to 26.144-145).
\item Page 495. (26.150). $J_y$ off by $-1$. ($J_x + iJ_y \ne J_{+}$) as is.
\item Page 496. (26.154). An extra $Y_{l'm}$ in the integral, in between $Y_{l' m'}$ and the $(\theta, \phi)$.
\item Page 498. (26.175). $e^{i\phi}$ should be $e^{-i\phi}$ in the first line.
\item Page 498. (26.178). An $\hbar$ factor has been lost in either (26.178) or (26.179).
\item Page 499. (26.190). minor: $\mathbf{j}$ should be $\mathbf{J}$.
\item Page 450. (26.192). minor: $\mathbf{j}$ should be $\mathbf{J}$, and $R$ should be $\hbar$.
\end{itemize}

# Chapter 27.

\begin{itemize}
\item Page 503. (27.8). minor: bold $\chi$. $R(\theta, \phi)$ probably meant to be $R(\chi)$.
\item Page 504. (27.20). Missing $\hbar E_n$ factor on LHS.
\item Page 507. before (27.53). minor: Velocity $v$ missing bold.
\item Page 510. before (27.78). minor: periods in the two kets should be commas.
\item Page 510. (27.80). $\sigma_y$ and $\sigma_z$ should be interchanged (if $\alpha$ is the polar angle then $\hat{\mathbf{n}} = \hat{\mathbf{y}}$ for that rotation, and $\hat{\mathbf{n}} = \hat{\mathbf{z}}$ for the rotation in the $x,y$ plane). The $\hbar$‘s here should also be dropped.
\item Page 511. (27.81). Same as 27.80.
\item Page 511. (27.83). $\hbar$‘s should be dropped.
\item Page 514. (27.109). minor: dot instead of cdot.
\item Page 515. (27.117). Same error as in (26.149-150). $\hbar$‘s missing, and wrong sign on $J_y$.
\end{itemize}

# Chapter 28.

This chapter written as if $\hbar = 1$, without a statement that this is being done.
\begin{itemize}
\item Page 518. (28.4). $\hbar$ missing. Also in text following, eigenvalue should be $m \hbar = \hbar (m_1 + m_2)$.
\item Page 519. (28.9). $\hbar$ missing LHS.
\item Page 519. (28.11). $\hbar$ missing (after each equality). Text following $m$ and $j(j+1)$ eigenvalues should be multipled by $\hbar$ and $\hbar^2$ respectively.
\item Page 519. following (28.14). $\hbar$ missing in $J_{-}$ equality.
\item Page 520. (28.15). $\hbar$ missing for two factors after last $=$.
\item Page 520. (28.16). $\hbar$ missing LHS.
\item Page 520. (28.21). $\downarrow \downarrow$ should be $\uparrow \downarrow$.
\item Page 521. following (28.25). Chapter 2 should read Chapter 5.
\item Page 522. (28.31). Notational inconsistency. ${\left\lvert {j_1 j_2 jm} \right\rangle}$ should read ${\left\lvert {j_1 j_2, j m} \right\rangle}$
\item Page 522. (28.31). Extra $\vert$ between braket and ket.
\item Page 523. (28.36). Notational inconsistency. $\left\langle{{m_1, m_2}} \vert {{jm -1}}\right\rangle$ should read $\left\langle{{m_1, m_2}} \vert {{j,m -1}}\right\rangle$
\item Page 525. following (28.52). $l(l+1)$, $s(s+1)$, $j(j+1)$ eigenvalues all missing $\hbar^2$.
\item Page 525. (28.53). LHS missing $\hbar^2$.
\item Page 525. (28.54). LHS missing $\hbar^2$.
\item Page 525. (28.57). RHS missing $\hbar$.
\item Page 525. (28.58). RHS missing $\hbar$. $m \pm \frac{1}{{2}}$ should be $m \pm 1$.
\item Page 526. (28.60). $\hbar^2$ missing from both terms.
\item Page 526. (28.61). In first term $\sqrt{l + m_1 + 1}$ should be $\sqrt{(l + m_1 + 1)(l - m_1)}$.
\end{itemize}

# Chapter 29.

This chapter written as if $\hbar = 1$, without a statement that this is being done.
\begin{itemize}
\item Page 531. (29.23). $\hbar$ missing from second two lines.
\item Page 533. (29.25). $\hbar$ should multiply all.
\item Page 533. (29.26). $\hbar$ should multiply all (RHS).
\item Page 533. (29.29). $\hbar$ should multiply all (RHS).
\item Page 533. (29.30). $\hbar$ should multiply all (RHS).
\item Page 533. (29.31). $\hbar$ should multiply all (RHS).
\item Page 536. (29.59). $\hbar$ should multiply RHS.
\item Page 536. (29.60). $\hbar$ should multiply RHS. ${\left\lvert {j m + 1} \right\rangle}$ should be ${\left\lvert {j, m+1} \right\rangle}$.
\item Page 536. (29.61). $\hbar$ should multiply RHS. ${\left\lvert {j'm' - 1} \right\rangle}$ should be ${\left\lvert {j', m'-1} \right\rangle}$.
\item Page 537. (29.65). $\left\langle{{j'm' - 1}} \vert {{m, q}}\right\rangle$ should be $\left\langle{{j', m'-1}} \vert {{m, q}}\right\rangle$.
\end{itemize}

# References

[1] BR Desai. Quantum mechanics with basic field theory. Cambridge University Press, 2009.