### Errors found since the third printing

Art ramirez comments that paramagnetism and ferro/antiferro
should really be on a diffent footing. So far, I see no easy way to
change this

## Errors still in the second printing that are (mostly) fixed in the third Printing (gone to press 2019)

might be good to quote phil anderson on page 3, from "More is Different". "The ability to reduce everything to simple fundamental laws does not imply the ability to start from those laws and reconstruct the universe." Or "The more elementary particle physicists tell us about the fundamental laws of the univese, the less relevance they seem to have..."
page 20 note 7. Mobility is always defined to be positive. (so it is missing a minus sign here)
page 22 note 9. There is a missing minus sign, it should read jq = -kappa grad T.
page 24, eqn 3.7. It should be -0.43 not -4.3. Incorrect by a
factor of 10
Page 38 Ex 4.5 should read k_B T << mu
page 54. The attractive potential V between electron and nucleus should have a minus sign.
page 55, margin note 14. We say "we will choose t positive" but then we go on to keep the general case on the next page of t possibly not positive. So the phrasing of note 14 probably needs to be changed.
page 63, there is a typo in the numertor of the 2nd order perturbation expression!
page 86 in the box, strictly speaking I mean eigenenergies En = ...
page 94 note 4. The word "are" is incorrectly repeated
page 109. Exercise 11.8. The symbol epsilon is used both for a small parameter and for an onsite energy!
page 113 fig 12.1 caption "of" is incorrectly repeated
page 114. May want to give the detailed definition of conventional unit cell see here http://reference.iucr.org/dictionary/Conventional_cell. Note: After detailed consideration, I think it is better to not give this more detaield definition as it assumes other knowledge that would have to be introduced.
page 114. Def 12.1.1, strictly speaking one needs to include subtraction as well!
page 116 "we show a periodic structure in two dimension" should be "dimensions"
page 118 add comment that [uvw] to a crystallographer means a direction in real space
page 122. In fig 12.19 it says within the figure for monoclinic "alpha=90, beta=90, alpha not equal 90, only two right angles". It should be gamma not equal 90.
Page 132, second paragraph "To represent a family of lattice plane, one should take...." should be "lattice planes."
Page 136, "Then we make a straight line from X to K, and then X back to Gamma". Last part should be "and then K back to Gamma"
Page 142-143. There is a switch of notation. in 14.2 it says k'-k=G whereas on the next page it is k-k'=G. In some sense this doesnt' matter because if G is a recip latt vec then so is -G, but maybe better if it is consistent? After some thought i think I'm not going to change this either. There seems to be good reason in terms of conventions to leave k as it is and k' as it is in both cases, so we just have to deal with the fact that notation of what we call k and what we call k' sometimes switch.
Page 145. Might mention that in an ionic material Z does not count the electron that has been lost!
Page 146. Stefano Bonetti (an x-ray guy!) points out that the list on page 146 seems to indicate that neutrons are always better than X-rays and neglects a number of modern developments in x-ray technology that enable them to do some impressive experiments. Add a footnote somewhere!
Page 148, section 14.2.2. First example two errors. It says wavelength 2pi/a. This should be wavevector (or wavelength a). Furthermore, it isn't a, the extra path length for back-reflection should be 2a, not just a (just a diffraction grating, you have to go an extra a down and an extra a up).
page 151 4th line from top. Should say Fig 7.1 not fig 7.
page 160 Q. 14.5 some minor typos. In the phrase Avagadro's number, the words should be separated by an apostrophe not the prime symbol, Furthermore,Avagadro should be written as pAvogadroq. And perhaps Cu–Ka should be Cu–Kalpha. Speaking of useless typos, the en-dash (–) in phrases Debye–Scherrer and Cu–Ka should probably be the shorter hyphen (-), since they are compounds (e.g. red-green) and not ranges (e.g. 34–60). (Thank you Jakob Kastelic)
page 173 just below the figure, should say "number of k states is equal to number of PRIMITIVE unit cells in the system". Note same thing on page 135!
Somewhere in Chapter 17, I should comment that the room temperature resistivity of copper versus diamond differ by some 20 orders of magnitude! (maybe it fits bottom of page 174, with the footnote position on page 175).
somewhere around page 184. Perhaps worth mentioning that postive energy for pushing a hole under water is really the same as saying we had to push an elelectron up. Note sure where to put this. DECIDED NOT TO MAKE THE CHANGE. NO space in text.
page 189 Rydberg should be e^4 upstairs not e^2.
Page 196. question 17.4. It should say "energy density of electrons in the CONDUCTION band"
Page 196. question 17.8. It should be MINIMUM not maximum. But it is easy. Maybe it should not have a star.
page 201 footnote 16 absorBtion should be written absorPtion
Page 209 section 19.1. It might be worth noting taht suscpetibiility can be defined differentially dM/dH in cases where M is nonzero. I tried to find a place to include this, but it didn't seem to fit anywhere. It is actually in exercise 22.7 though -- maybe this is enough?
page 211, 2nd paragraph third line, "magentic" should be "magnetic"
p212, the line above sect19.2.1, "S is the spin component of J", strictly speaking J is a quantum number, just an integer, so it does not have components, so S cannot be a component of J. Perhaps these should be bold so as to indicate they are operators.
p212 footnote 13, the subscript of l should be italic not bold (occurs three times!)
p212, LHS of the eqn below "Naive Argument", the indices (namely, 1 and 2) of sigmas should not be bold
p213, the eqn on top of the page, the second arrow should probably be an equality sign (a limit is a well-defined number, and not something that tends to something). I KNOW IT IS IMPROPER USE, BUT I"M GOING TO STICK WITH IT!
p217. In footnote 24 it says "muK" not "micro K"
p223. 19.3 typesetting. Names of orbitals (s, p, . . . ) should not be italicized. Also, you use a hyphen in p-shell, but then inconsistently omit it in l shell. — There should be no full stop within the parentheses. 19.5
The m in 10^20 m−3 should not be italicised, for it is a unit. The ∗ in m∗ should be superscript.
p228 eq 20.4 perhaps it should be footnoted that Sx^2 + Sy^2 + Sz^2=1 which is why we use an exponent of 4.
p233 footnote 1. There should be 2 in the denominator of the magentic energy.
p235, the paragraph left of footnote 5, "the -JSi.Sj. term" (the second
dot should be removed)
page 237. Eqn above 21.2. The M_z should be subscript not superscript.
p240. QUestion 21.1c. Question mark should terminate first sentence.
p246, sect22.2.1, above the 1st eqn of the subsection, "Eq.22.3" (space seems to be missing after the period)
p247 sect22.2.2, last line of the Aside, "anitferromagnets"
page 250, exercise 22.7 "magentization"
Page 256. The U -> Infinity limit is tricky. In the thermodynamic limit it is only U = infinity. This is discussed in the excerise 23.3. THE ISSUE IS TOO SUBTLE TO COMMENT ON HERE
page 260. Exercise 23.3. When i discuss the kinetic energy of the hole, it isn't clear that I have the sign right -- because you can treat holes as being either positive or negative energy depending on convention. Maybe there is a better way to write the problem which won't be so confusing. (Maybe I should talk about "total kinetic energy" or similar?)
page 266 "under a 90-degree rotation" might be better, "after" or similar?
page 273 absrorption not absorbtion twice in the 2nd to last paragraph.
General typesetting: many instances: in equations, variables but not descriptive labels should be italicized (thus for instance $\psi_{orbital}$ should be $\psi_\text{orbital}$). Question on unit typesetting: Should there be a space between 300 K or should it be 300K for clarity? General typesetting. Lots of dashes should be hyphens : Born--Oppenheimer, etc. Born-von-karman, etc. Check the index.
page 160 Q 14.8. More typesetting. f_{Cu} and f_O the subscript
should not be italic. Fix this only if I fix all the other subscripts
in chapter 14! Not making this change.

# Errors in the First Printing that Have Been Fixed

## Known Serious Errors in the Main Text

Figure 7.1 left hand side is borked in many printings for some reason (BOO!!!). The figure is supposed to look like this . (Not my fault!!! it looked correct in the proofs!)

Page 117, Figure 12.9. The labels a1 and a2 are exchanged.

Footnote 3 on page 176, there are some stray factors of 2 in the expression for the energies. In both places it should be (pi)^2 not (pi/2)^2.

Top of page 214 (section 19.2) The pluses should be in the first equation and the minues should be in the second equation (compare to the bottom of previous page).

### Less Serious Errors in the Main Text

Just before Equation 2.1, page 8, it says "the eigenstates.. are". Really it means "the eigenstate energies ... are".

Page 23, footnote 11. Both sigma and kappa have dimensions appropriate for a two dimensional system, not a three dimensional system. sigma should have units 1/(Ohm-meter) and akpps should be W/(meter K).

page 33, margin note 18. Actually Newton was ranked 0 and Einstein 0.5, not the other way around. (Actually I'm still working on confirming that Newton was ranked 0. Need to do some research here).

page 43 footnote 11, "once we change the potential" not "changes"

Page 55, there is a bit of confusion about when we take t to be
generally complex, and when it is real. In fact we can always choose
the basis states |1> and |2> such that t will be real in this case.
I should clarify this somehow.

section 6.2.2. It should probably say in footnote 13 that t has dimensions of energy. (Just to clarify).

End of page 56 and page 57. Unfortunately the letter r is used for both distance between atoms and the distance between the nucleus and the electron!

Section 6.3 on Van der Waals forces. Really we should also talk about dipole-dipole forces between molecules with permanent dipole moments --- as well as dipole-induce-dipole forces between a molecule with a permanent dipole moment and one that has none. What is discussed here is entirely about forces between two atoms or molecules with no permanent dipole moment.

Page 60. In the table, description column under "Molecular" the "Dipole" moment should be fluctuating or temporary.

Page 66, footnote 1, James Heath was not included on this Nobel Prize. It was Robert F. Curl who was awarded the prize along with Kroto and Smalley

Page 80 (section 9.1 Aliasing). The first sentence has the word "same" repeated by mistake

Page 90. I should clarify that if the light and dark masses are atoms then it would not make sense to have alternating springs, since each spring connects a light atom to a dark atom. However, if the masses are molecules (not spherically symmetric) then it makes sense that the bond to the left and the bond to the right can be different. In more detail one could comment about dimerization and Peierls instability but this is "beyond the scope" of the course.

Footnote three page 115. This is equivalent to det [m] = 1, or -1.

Equivalent Definition 12.1.1. This definition would allow, for example, the real numbers to be called a lattice. One can fix the problem by insisting on a finite number of lattice points per volume.

page 125. References "crystals" not "crystal"

The equation before 13.6 appears to be missing a factor of the unit cell volume in the denominator (2pi)^D/v. Compare to Eq. 13.5 before it.

Fig 13.7, it might be better if the caption said "wavevector" rather than "momentum".

Footnote 7, page 142. William L. Bragg is no longer the youngest ever Nobel Laureate. Malala Yousafzai was awarded the Nobel Peace Prize in 2014 at age 17.

Page 148. It would be good to insert a footnote stating that the lattice selction rule only tells you what must vanish. It is possible, due to the structure factor for the basis, that other reflection peaks also vanish. Silicon is a good example of this.

page 153. It might be worth explaining why d = lambda/sin(theta) and not n lambda/sin(theta).

page 153 and thereafter. It is a bit of annoying notation that I use a,b,c,d to label the peaks instead of 1,2,3,4 which would be better. The reason this is a problem is because "a" has been reserved for the lattice constant already, and then d_a looks a bit strange. We've used "a" in two senses. Probably I should switch notation here! (NOTE: I fixed this in the next edition and changed notation on page 153, 154, 155 accordingly)
p. 156. Fig. 14.11. Note that for disordered materials S(k) is actually average of sum_{i,j} e^{i k (ri - rj)}. if you tried to take just average of sum_i e^{i k r_i} it would come out zero
p. 157. The discussion on inelastic X-ray scattering not being useful is not really correct any more. (Thanks to Phil Allen for pointing this out).
Page 166 equation below 15.10. Here the ket |k'> should be e^{i k' x} or e^{-i k x} but not e^{-i k' x}.

Figure 16.3 is quite a crude sketch. Probably I should do a better job with these.

p. 215, paragraph below eq. (19.5), “these moments aligns with the B-field”, aligns should be singular.

p. 226, fig. 20.1 caption, “magentization” misspelt.

p. 229, side note 14, “was solved in by Ising in 1925”, first “in” shouldn’t be there.
p 229. Might want to add a comment that some certain features of the 3d ising model have recently been calculated exactly!
p. 246, section 22.2.1 first sentence, “magentization” misspelt.
p. 251, last sentence of first paragraph “antiferromagentism” misspelt.

p. 252, Eq. 23.1. I should add a footnote noting that you can't have two electrons with the same spin on the same atom and this is why you only have spin-up to spin down interaction.

p. 265. The top equation is incorrect. The last exponent should be k+h, not k+l.
p. 258. Useful also to comment here that t has dimensions of energy.
#### Corrections to the Exercises

Comment: With apologies, the reason there are so many problems with exercises is because only about half of them have been tested by real students. Hopefully none of the errors are too major and the errors won't take away the usefulness of the exercises.

Exercise 2.8. It would probably be better if there were a 3 out front of the formula. The forumla as written is appropriate for a 1d situation. But then you are asked to apply it to 3d. So probably better to think about 3d from the start.

Exercise 3.2 Resistivities on the table should be 10^{-8} not 10^8 (16 orders of magnitude off here!)
Exercise 3.2. Last part should say room temperaature AND PRESSURE.

Exercise 5.2. OK, maybe it is a bit overstating to say that the agreement is very good. Try declaring p orbitals to beoutside of s orbitals and see if the agreement gets better!

Exercise 9.5. The ansatz form looks a bit strange as I have unfortunately labeled the wavevector on the left as k_R and the one on the right is labeled k_L. Sorry about that. It would be less confusing the right way around.

Exercise 9.6. The wavevector q needs to have both real and imaginary parts.

Exercise 9.7.i It should say that omega_m^2 is the mth eigenvalue.

Exercise 10.5.a. It would probably be a bit better if it said frequencies rathter than energies.

Exercise 11.4. It should say "if the atom is divalent" not "diatomic". Oops.

Exercise 11.7. (i) Just after the first equation, I use epsilon for energy, whereas everywhere else in the problem it is E. These are supposed to be the same symbol. The way j is written it is a particle current, not an electrical current. It should have an additional factor of -e to become an electrical current. One should also always assume temperature much less than mu.

Exercise 11.8. The decrease in kinetic energy should be x^2 log x. Not linear in x. But it is still larger than x^2. This problem really needs to be walked through carefully as it is not very easy to find the x^2 log x!

Exercise 13.2. It should say (210) family of planes. Not family of lattice planes.

Exercise 14.4. The scattering lengths of Na and H are in units of 10^-5 nm not 10^5 nm. (doesn't really change much in the problem)

Exercise 14.5. There angles are theta not 2 theta!

Exercise 15.4. Presumably we should write k or q instead of G since these are not reciprocal lattice vectors!

Exercise 15.6 Another mess. In part (a) presumably one is meant to show psi(x) = e^{i k a} psi(x+a). Then it should be psi(x) which takes the form A sin(qx) + B cos(qx) not u. And finally in the second to last equation, k should appear only in the exponent. The factor out front of the brackets should be q_E not k. AND the expoent is e^{-i k a} not e^{i k a}. I'm not sure how many martinis I must have had when I wrote this problem. Ugh.

Exercise 17.2c. should say "the relationship between charge carrier concentration AND TEMPERATURE"

Exercise 18.4. It should be epsilon_c1 > epsilon_c2 (!!!)

Exercise 20.2 Probably should state all of the spins are the
same length.

Exercise 19.2b Counting of electrons is wrong for Europeum.

Exercise 19.6 "monatomic atoms" ? Stupid stupid stupid. Should say monovalent. Should also probably specify $g$ factor.

Exercise 20.4 Obvious typo: It should say 2 s1 dot s2 = (s1-s2)^2 - s1^2 - s2^2

Exercise 20.5 The H in e^{- Beta H} should be caligraphic

Exercise 20.6 Probably the last part should ask for the
magnetic moment per spin, and should ask you to only calculate it for
small h so that you can get the suscpetibility. The general
expression is a bit messy (although certainly possible).

Exercise 21.1 part c "where might it go". Maybe this need to be more specific?

Exercise 21.2d. You don't need to estimate any other parameters (despite what it says)

Exercise 21.3. It is better to write the first equation as +sin^2 rather than -cos^2. These differ by a constant. However, the former has zero energy when the spins are aligned in the favored direction. (Also the text needs corresponding correction)

Exercise 22.2. The "where there are N total lattice sites in the system" is stated twice. Redundant.

Exercise 22.4. Maybe remove comment about "express in terms of " for part b. I don't know what i was thinking here.

Exercise 22.9 Maybe add an exercise on susceptibility below Tc for a ferromagnet?
#### Plus this is a list of tiny typesetting errors just so I don't forget to fix them!

exercise 6.6 just before part c, there is a < that should be a \langle (yes, they are very similar, but might as well fix it!)