Errata: Quantum Mechanics

Errata for Quantum Mechanics

Here is a list of typos and corrections that I know about.

Chapter 1

Page 13: Above (1.11), "Bit here's" should be "But here's".
Page 23: Figure capture "show" -> "shown".

Chapter 2

Page 36: With the definition of the Gaussian, the width in the figure should be 2\sigma^2 instead of 2\sigma. (The \sigma defined in A(k) is not the usual standard deviation.)
Page 45: The b_n in the middle equation should be b_p
Page 51: In (2.86), the inequality should be -a < x < a. (Not -a < 0 < a which is just dumb.)
Page 59: In (2.120), the d^2\psi/dx should be d^2\psi/dx^2
Page 54: Below (2.98), the phrase "red circle" should just be "circle". (Because the figure is in black and white!)
Page 62: In (2.127), the correction should be O(x^3)
Page 66: Below (2.136), the density of the beam should be |A|^2, not A.
Page 68: In (2.146) one of the equalities is repeated twice.
Page 69: In (2.153) another place where it should be -a < x < a

Chapter 3

Page 84: In (3.50), \psi_n on the RHS should be \psi_m
Page 90: In (3.72), in the third expression a_n should be a_m
Page 91: Just after (3.77), it should say ||\psi||^2 = ...
Page 102: In the first line of (3.134), the exponent is missing a 1/hbar
Page 104: In (3.141), there should be a -hbar^2 in front of the middle expression.
Page 105: Below (3.147), the operators are missing their hats in [A,B]=0
Page 109: In (3.167) the e^{-ax^2/2} should be e^{-ax^2}
Page 111: Below (3.176), the "Ricci tensor" should be the "Ricci scalar".
Page 114: The last term in (3.186) should have an absolute value
Page 117: Equation (3.192), the LHS should have the state \ket{\phi} \otimes \ket{\psi}
Page 117: Above (3.196) the tensor product should be C^2 \otimes C^2 (i.e. the times symbol should be in a cirlce)

Chapter 4

Page 133: The x- and y-axes in Figure 4.1 should be swapped
Page 138: The Hamiltonian in (4.49) should be dressed with a hat.
Page 140: Equation (4.56) should be (1-\pi^2/(8n^2))^2 \approx 1- \pi^2/(4n^2). Then the following equation (4.57) should be (1-\pi^2/4n^2)^n \approx 1-\pi^2/4n.

Chapter 5

Page 145: Below (5.22), the expression for a^\dagger is missing the normalisation 1/\sqrt{2m\hbar\omega}. The result in (5.23) is unchanged.
Page 150: There is a minus sign missing in the (irrelevant) overall phase, which should be e^{-i\omega t/2}, in (5.44) and (5.45) and in the paragraph between them.
Page 150: (5.46) should read <\hat{x}> = x_0 \cos(\omega t) + (p_0/m\omega) \sin(\omega t) and <\hat{p}> = p_0\cos(\omega t) - mx_0\omega \sin(\omega t)
Page 151: The direction of the arrow on theta should be flipped in the figure
Page 153: There should be an extra factor of 1/2 in front of the gamma function in the final expresison
Page 157: After (5.72), "follows from (5.68)" should be "follows from (5.67)"
Page 160: There should be no factor of 1/2\pi in (5.82). That also spills over to the first line of (5.83) where the 1/2\pi should be removed. (But it should still be there on the second line of (5.83))

Chapter 6

Page 164: The Laplacian in (6.2) is missing ^2 on the numerators
Page 174: Missing ^2 in the final derivative of (6.45)
Page 190: In (6.120), the middle term on the RHS should be - i\hbar \hat{p}/m rather than +.
Page 193: In (6.129) and (6.130) and (6.133), the Rydberg constant is denoted as R_H. But earlier in Chapter 6, it is denoted as Ry.
Page 194: In (6.137) (in the final term) and (6.139), the \epsilon_0 should be \epsilon_0^2

Chapter 7

Page 212: In (7.25), \hat{p} should be replaced by \hat{p}/\hbar
Page 219: There should be hats on the L operators in the sentence below (7.56).
Page 220: (7.64) should say R_3(\theta) = e^{-i\theta T_3}
Page 223: There should be a |j,m> on the LHS of the second equation in (7.70).
Page 224: The LHS of (7.77) should be the norm squared (the square is missing)
Page 225: In (7.87), the term e^{i\theta \hat{J}_3} should be e^{-i\theta \hat{J}_3/\hbar}. The minus sign should be in the next exponent as well.
Page 227: Better to put minus signs in the exponents of (7.90) to match (7.64)
Page 230: Below (7.97), the "Lagrangian (7.93)" should read "Lagrangian (7.92)"
Page 230: No factor of i in front of \delta_{\alpha\beta} on the RHS of (7.99).
Page 230: Below (7.101), there's a missing hat on the operator z_\alpha^\dagger
Page 236: In (7.129), the first two terms in the final line should have a factor of 1/2, so it reads (schematically) 1/2(J_+J_- J_-J_+). That then infects (7.130), which shouldn't have a factor of 2 in front of the J_+J_- + J_-J_+ terms. Finally, in (7.131), the second and third lines shouldn't have that factor of 2.
Page 241: In (7.152) the middle equation is |0,0> = but should be |2,0> =
Page 242: If we derive (7.158) from (7.144) then there should be an overall (irrelevant!) minus sign on the RHS.
Page 244: Above (7.165), the operator \hat{A} should be a bold A
Page 244: Below (7.166), hats are missing on the operators A_3 and A_\pm
Page 245: In (7.174), the second line has 2\hbar but it should be just \hbar.
Page 246: Just below (7.174), it says j \geq j+2 but should be j' \geq j+2
Page 246: Above (7.176), "azimuthal angle" should be "azimuthal angular momentum".
Page 246: In (7.177), the first term on the second line should have an extra \hbar in front
Page 247: Below (7.182), there are missing hats on the operators U and T
Page 247: Below (7.184), there's a missing hat on the operator p
Page 255: Below (7.216), in the sentence in parantheses, the |\psi(t)> should be |\psi(-t)>
Page 256: Below (7.219), H\Theta|\psi> = -\Theta H|\psi> = -E\Theta|\psi>. (The \Theta is missing in the final term.)
Page 256: Below (7.222), there's a missing hat on the operator B
Page 257: Below (7.233), there's a missing hat on the operator H
Page 262: In (7.252), the spin operators in the equations on the left should be multiplied by 2/\hbar

Chapter 9

Page 292: Below (9.51), the Hamiltonian should have a minus sign.
Page 300: There's a factor of \hbar^2 missing in (9.80)
Page 302: The semi-direct product symbol in the text below (9.84) should use the latex symbol \ltimes, not \rtimes. That means that the vertical line should sit on the left-side of the bow tie, not the right.

Chapter 10

Page 320: Below (10.36), the \log n \approx should be \log n! \approx
Page 320: In (10.37), the prefactor after the = has a minus sign wrong: it should read (\log(c\lambda) + \log n)
Page 321: Second paragraph, last sentence: "example this" -> "example of this"
Page 321: Just before Section 10.1.4, there is a e^{-1/\lambda^p} which should be e^{-1/(c\lambda)^p}
Page 323: Third paragraph, third line: the second "P_\perp |\psi^0_i>" should be "P_\perp |\psi(\lambda)>"
Page 325: There is a sentence below (10.55) that says you can show P|\psi_i^1>=0. This is a little bit misleading. The correct statement is that it's possible to choose a \lambda-dependent unitary operator on the degenerate subspace that sets P|\psi_i^1>=0
Page 328: In (10.69), the O(\epsilon^2) should be O(\epsilon^3)
Page 333: In the "Do Bound States Exist" section, the Coulomb potential should be -1/r, not +1/r
Page 346: Just before "An Aside: Quarkonium", the x \rightarrow \infty should be u \rightarrow \infty
Page 347 and 348: The 1/2m in front of (10.138), (10.139), (10.140), and (10.141) should be inside the (...)^{1/4} bracket.
Page 348: In both (10.139) and (10.141), the denominators of the two prefactors should be E-V(x) (and not V(x)-E)
Page 350: In (10.144), inside the square-root on the LHS there's a m^2 that should be m
Page 350: In (10.147), the E^{1/4} on the second line should be E^{3/4}
Page 350: In (10.148), the 1.75\pi should be \pi/1.75
Page 351: There's a factor of 2 missing in (10.156) in both the middle and final term. The factor in the middle term should be C\pi/2 and the last term should read C\pi/v.
Page 353: In (10.160), it should be V(x') in the integrand

Chapter 11

Page 358: In (11.13), \dot{\lambda}^i is missing the superscript i
Page 367: The hydrogen molecule should, of course, be H^+_2, not H^-_2!
Page 368: Above (11.51), the \Psi_\pm should be \phi_\pm
Page 370: There's a factor of m missing in the x^2 term in both (11.57) and (11.59)
Page 371: Just after (11.58), the \tau << \hbar/\omega_0 should be \tau << 1/\omega_0
Page 374: There's an = sign missing on the right of (11.75)
Page 376: Equation (11.84) is missing an i\hbar on the left hand side.
Page 378: In (11.93) there should be a subscript I on |\psi(t)>
Page 380: In (11.97), it should say that it's the second term that dominates, not the first.

Chapter 12

Page 390: Above Section 12.1.3, the minus sign is missing in E_{ground} = -mc^2(Z\alpha)^2/2
Page 392: A series of unfortunate minus signs, starting in the text above (12.32) which should read E = -B.m = +(e/m)B.S. This then follows through to (12.32) which should be + instead of - on the RHS, and (12.33) and (12.34), both of which should have + in the first term.
Page 393: In (12.31) \omega_T should be bold.
Page 393: Above (12.37), it should say |nlm_l> instead of just |nml>
Page 398: In (12.57), it should be p^2V + Vp^2, not -Vp^2
Page 415: Below (12.91), it should say "three spin-triplets", not "nine spin-triplets".
Page 416: In (12.92), (12.93), and (12.94) an overall factor of e^2 is missing
Page 420: Below (12.102) and above (12.103), there is a U(x) that should be U_{\sigma_a}(x)
Page 421: In (12.105), it should be e^2/8\pi \epsilon_0 on the right-hand side (not e^2/4\pi \epsilon_0)
Page 424: In the first paragraph, it should say swapping "columns", not "rows" of the matrix

Chapter 13

Page 428: The electron mass m in (13.1) would be better written as m_e
Page 438: There should be a minus sign in (13.39)
Page 439: There should be a minus sign in (13.40)
Page 439: In (13.41), the F should be capital in the denominator
Page 442: In the second equation of (13.47), the first term on the right hand side should be <\psi_2| \Delta H|\psi_1>. (i.e. swap \psi_1 and \psi_2.)
Page 454: In (13.92), the left bracket should come after the \hbar \omega. In addition, the factor of 1/2 is then dropped when deriving the next equation on the grounds that it is common to all states, including the ground state.
Page 457: Below (13.104), the \epsilon should be \hbar \omega_0.

Chapter 14

Page 466: Equation (14.10) shouldn't have the factor of 2 in the denominator
Page 467: Above (14.19), it should say x=\pm a/2
Page 489: Above (14.110), it should say P_l(1)=1 (i.e. the subscript is missing)
Page 506: Above (14.181), it should say y>0, not r>0
Page 510: In (14.199), the exponent should be e^{-iq.x} rather than e^{+iq.x}, although the result is the same either way.

Chapter 15

Page 530: Missing minus sign in the exponent of (15.27)
Page 532: Below (15.37), it should be "n separate" instead of "N separate".
Page 532: Below equation (15.38), it should say we shift to integration variable \vec{x} - A^{-1} \vec{y}
Page 547: In (15.97) and the un-numbered equation above, the argument of K should be -i\hbar \beta rather than just -i\beta
Page 548: More of an addendum than a correction: the zeta function has a pole at s=1.
Page 554: In the un-numbered equation at the bottom of the page, there's a missing 1/2 in the exponent on the right-hand side.

Chapter 16

Page 569: Above (16.17), it should be P(s^A_i,s^A_j) (It's currently missing the subscripts.)
Page 570: The end of the first paragraph should read "The experiment was first done in the early 1970s by Clauser and Freedman, and more definitively by Aspect. It has been repeated many times since, with different groups trying to finesse the experiments in order to close off increasingly preposterous loopholes that philosophers claim to have discovered in the argument. Aspect, Clauser, and Zeilinger won the 2022 Nobel prize for these efforts."
Page 572: Equation (16.28) should read <A_1B_1> = <A_2B_1> = <A_1B_2> = ...
Page 595: It should be a sum over j in (16.96)
Page 596: Paragraph below (16.104) "two parts of the system", not "two parts of the subsystem"
Page 597: First paragaph "enlarged Hilbert space H", not "enlarged Hilbert space H_B"
Page 613: In equation (16.157), the arguments of the matrix M should be \delta t, not t+\delta t

Chapter 17

Page 634: I am mortified to learn that I spelt Richard Jozsa's name wrong in the Deutsch-Jozsa algorithm (and in the acknowledgements). It's Jozsa, not Josza. My embarrassment is compounded by the fact that Richard's office is four doors down from mine.

Chapter 1

Chapter 2

Chapter 3

Chapter 4

Chapter 5

Chapter 6

Chapter 7

Chapter 9

Chapter 10

Chapter 11

Chapter 12

Chapter 13

Chapter 14

Chapter 15

Chapter 16

Chapter 17

Further Reading