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Math, physics, perl, and programming obscurity.

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.

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