I will be grateful to all readers who point out errors, large and small. Small errors such as those listed below will be corrected every time the book is reprinted.
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A corrected printing was issued on February 16, 2001. The words "Corrected Printing" appear on the cover, making it easy to identify. Most of the errors identified in the first printing have been corrected. As new errors are identified, they will be recorded in the separate error pages for the first and second printing.
p. 7, It reduces confusion to speak of 60 degree rotations of the hexagonal lattice rather than 120 degree rotations. The two are equivalent since a clockwise 60 degree rotation can be produced by an inversion followed by a counter-clockwise 120 degree rotation.
p. 8, Basis vectors in figure have been adjusted to bring them into accord with the text
p. 34, S_6, C_{3h}, and C_{6h} should have no mirror planes containing the main symmetry axis; all radial lines should be dashed.
p. 39, Problem 6, set the distance between nearest neighbors to 2
p. 47, Between Equations (3.9) and (3.10) the end of the first sentence reads, "it is possible drop," so it needs a "to."
p. 49, in Equation (3.18) exp[i K.R]
p. 51, in description of {ijk} it is clearer to speak of “complete collection” than “family;” in contrast with <ijk>, {ijk} does not include planes related to (ijk) by rotational symmetry.
p. 60 and 61: a thermal neutron of 1 A has an energy of 0.08 eV; orders of magnitude are better indicated by saying that a 2 A neutron has energy of 0.02 eV. And while we're at it, better make the typical X-ray energy 12 keV, and the typical electron energy 60keV, although in the world of “Typical,” 60=100.
p. 63, The caption of Figure 3.14 has "an a crystal" in the second sentence.
p. 66, Problem 4, the figure is missing 3 spots, at locations corresponding to Bragg angle of 18.4 degrees. Download corrected figure here (8K, pdf, 24K PostScript)
p. 67, Problem 7 has a part a) but no b).
p. 84, Problem 5, part (a), index l_x varies between 0 and 200.
p. 99 In Equation (5.24), \xi should be a vector. In Equation (5.25), the bracket should be applied to Cartesian components:, <\xi_\alpha(0) \xi_\beta(t)>, with a discrete delta function on the right demanding that \alpha and \beta be the same.
p. 126, program fragment at bottom of page, “minimum” should be “maximum”
p. 129, the sum you need to form in part c) is \sum_j n_j \hat e_j
p. 137 in equation (6.2,) r_r is r_1.
p. 140, all all --> all
p. 152, problem 7 n dimensions should be d dimensions.
p. 156 R is a Bravais lattice vector
p.158, equation (7.14), the left side should have a u(r) multiplying H.
p. 160 a wave equations --> a wave equation. In Equation (7.29), remove L.
p. 161, Equation (7.33) remove L^d.
p. 162, Equation (7.39) remove L^d.
p.164, figure 7.4, the reduced zone is missing a tiny part of the band at the top from E=9..10.
p. 168, last paragraph, “should compared” should be “should be compared”
p. 174, first sentence after (7.83) has "a single off-diagonal elements..." Equation (7.83), (n) should be (m)
Wave Packets: There have been more queries and complaints about wave packets than any other single topic in the book. I am hoping that with a few extra words, I can help clear up some of the confusion. Comments on whether the extra words help or make things worse are welcome! Click here for extra comments on wave packets (90 kB, pdf) (104 kB, PostScript)
p. 163, first line, r-->R.
p. 166, (7.60) can be written --> (7.59) can be written
p. 167, Equation (7.69), the sum acts on the entire left hand side.
p. 185, the second paragraph of the introductory section has "could alway be" in the middle of it.
p. 188, In Equations (8.21), (8.22) and (8.23) energies E are measured relative to U_0.
p. 189, fifth line from bottom, “closer the origin” should be “closer to the origin”.
p. 190 Top line on page, n-1 should be n.
p. 191, four lines from the bottom of the page has "not be be"
p. 198, in the discussion following Equation (8.40) the hopping parameter t should be replaced by its absolute value.
p. 199 In problem 3, “a pictures” is “pictures.”
p. 200, Problem 6, the sum acts on everything to the right.
Tight Binding: The introduction of the tight binding model is somewhat obscure, and raises more questions than it answers. I have written some extra notes on the tight binding model. Click here for extra comments on tight binding models (60 kB, pdf) (88 kB, Postscript)
p. 204. Equation (9.4) will be derived in section 9.2.1, but one can begin by simply writing it down in the spirit of Equation (6.3).
p. 207, Equation (9.21); the final delta function is confusing. According to Equation (9.10), two particles have the same spin if they share the same function $\chi_l(\sigma)$. The final delta function is meant to indicate that there is a factor of 1 if particles i and j both have the spin-up or spin-down function, and a factor of zero otherwise. The proper notation would be [\sum_\sigma \chi_i(\sigma)\chi_j(\sigma)], but this doesn't fit on one line anymore. I think that pages 206 through 209 are a great argument for second quantization. In Equation (9.22), need parenthesis around argument of first integral.
p. 208, midway down, E^*_{ij} should be E^*_{ji}
p 211 top line of text, too many “linears” around KxK.
p. 214, Equation (9.48) put parentheses around argument of sum.
p. 219 A perceptive reader asks about the “freedom” to modify the exchange-correlation term in Equation (9.80). How can there be any freedom to modify such a thing in what is supposed to be a first-principles business? Are we not deriving behavior of matter from the fundamental knowledge of quantum mechanics? And yet there is indeed freedom, if only judging by the many modifications and variants of (9.80) that have appeared over the years. There is a gap between the rhetoric of performing first-principles calculations, and the reality, which is that Equation (9.1) is completely intractable, and replaced by other equations. Applied mathematicians coming to physics tend to assume that there must be some rational basis for choosing approximations to (9.1); some small parameter in which one expands, keeping terms to some order. There is no such thing. There are physical arguments, and approximations found through trial and error to reproduce some quantities in agreement with experiment. Anyone who holds this process in contempt is welcome to try to find something better, but should be warned that a large segment of the physics community has worked for over 40 years to improve dramatically upon (9.80) without much success, and (9.80) won Walter Kohn the Nobel Prize.
p. 223 In Problem 2(a) include a term that accounts for the interaction energy of the positive background charge with itself. This constant offset has no effect upon the Hartree-Fock equations.
p. 225, Equation (9.102) should have e^2.
p. 233, Equation (10.11) Forgot integration measure \sin\theta in right hand side equation.
p. 234. One reader gently
suggests that a sentence near the bottom of the page is so abominably
written that I should be shot. The sentence in question is “The
pseudopotential can handle these by generalizing the Kohn—Sham
equations so that they solve the Dirac equation, and then arranging
for the solution of Schr\"odinger's equation for the
pseudopotential to produce wave functions and energies matching
solutions of the Dirac equation for the original potential.” The
reader suggests that I greatly expand the sentence. I cannot fit the
expansion in this edition of the text, but put it here:
"For
heavy atoms, relativistic effects become important because electrons
near the nuclei move at speeds that are a significant fraction of the
speed of light. The electron wavefunctions near the nuclei must
therefore be described by the Dirac equation. However, the
pseudopotential method can also be applied here. To determine the
radial wavefunctions, one must work with a generalization of the
radial Kohn-Sham equations (10.9) that correspond to the Dirac
equation. The previous steps in creating a pseudopotential are now
modified as follows:
Step 1 on page 232 is the same except that
one must write down and solve a version of the Kohn-Sham equations
that generalizes the Dirac equation, rather than the Kohn-Sham
equations presented in the text.
Step 2 on page 233 is unchanged;
again, one draws smooth replacements for the original wiggly wave
functions.
Step 2 on page 233 is unchanged. One can take the
original nonrelativistic Kohn-Sham equation in (9.79) and put a
pseudopotential in it that produces the wave functions obtained in
the previous step. Now the pseudopotential is not only compensating
for the smoothing procedure of step 2 that removed wiggles from the
wave function, but also is compensating for the differences between
the Dirac equation and the Schroedinger equation. That is, the
pseudopotential is chosen to produce a wave function for the
Schroedinger equation that is also a solution of the original Dirac
equation.
p. 237, Equation (10.24), U^{at}(r) should be U^{at}(r+\delta)
p. 239, All occurrences of \vec a should be \vec a1. Second paragraph, third line, “that that” is “that”.
p. 250 The free electron bands in Figure 10.7 were a little sloppy. An improved figure is here (pdf, 8K)
pp.
251 and 253. Figures 10.8 (b) and 10.10 are in error. Furthermore the
discussion that surrounds them does a disservice to the authors of
the program VASP that I employed to produce portions of these
figures. I owe the authors an apology. So, first, I would like to
state that VASP is not only reasonably priced, impressively fast, and
relatively easy to use, it does not make the type of
elementary error shown in Figures 10.8 (b). The error is mine. It is
due to tracing out locations in k space different from those
labeled on the figure. When the correct k space points are
employed, the figures improve dramatically. Two unanticipated
phenomena contributed to my error. The first was a program feature
that was very sensitive to a single ill-placed blank space in an
input file. The second was a charming eagerness of band-structure
experts I consulted to assume that programs written by others do not
work properly. Corrected versions of the pages can be obtained
here:
Page 251 (PostScript,
PDF)
Page
253 (PostScript,
PDF)
*p. 256. Top line: the best fits are d=0.35, Rc=0.943, U0=-31.30 . Once these changes are made, all the numerical values on pages 256 and 257 change, although they are correct given the values that have been suggested. The final graph on page 258 changes as well, although the alterations are difficult to make out by eye. If you prefer to carry out the problems with corrected values of the pseudopotential, obtain corrected pages here (pdf, 28K) Note that in parts (e) and after, all energies are in Rydbergs, not eV.
p. 258. In 7b, “needed determine” should be “needed to determine”
p. 268, Table 11.4, the final digits of entries in the table were computed in single precision and are incorrect. The correct values are
Crystal fcc bcc hcp
A_6 14.4539 12.2537 14.4549
A_{12} 12.1319 9.1142 12.1323
A_6^2/2A_{12} 8.6102 8.2373 8.6111
p. 275, middle of first paragraph. I mean to say that rs/a0 would need to be much less than 1 for the high density limit to apply, but with actual values of 3 it is not.
p. 276, after Equation (11.38) the reference should be to Equation (11.37).
p. 277, Equation (11.40) replace G by Ga.
p. 278, Equations (11.45) and (11.47) replace Ekf0 everywhere by 2Ekf0.
p. 282, second line of 11.8 “reply” should be “rely”.
p. 284, Problem 5, “many many” should just be “many”
p. 295, after Equation (12.38) \omega t should be i\omega t.
p. 308, line 10 should refer to Equation (6.7), not (6.8). Comment to Eq. (13.10), replace K by −K
p. 316, Equation (13.43), sum over i, not l.
p. 318, Equation (13.53) in the exponent, n should be l.
p. 319, Equation (13.59) is missing factors of 1/V before first two sums. In Equation (13.61), N denotes number of terms in sum (13.58), which for a monatomic lattice in three dimensions is three times the number of ions.
p. 320, “several simplification”--> “several simplifications”
p. 325, in Equations (13.80) and (13.81), what is being calculated is V\beta, not \beta.
p. 335, top paragraph, long-wavelength vibration and not zero-point motion destroys Bragg peaks.
p. 338, Figure 13.19(A), swap labels --1/2 and 1/2 in the lower part of the figure; note that the g factors for the ½ and 3/2 levels have opposite signs, so the levels have to be ordered differently. Equation (13.130), take integral from 0 to \infty, and change sign of argument of second exponential.
p. 340, Problem 6, part (b), it is Eq. (13,119) that diverges.
p. 351, Equation (14.9), the nearest integer function is given by int (x/a+1/2).
p. 416 Equation (16.14) should refer to (16.12) and (16.16) should refer to (16.11). Factor of 2 is missing in Equation (16.17)
p. 421, Equation (16.38) one occurrence of k is missing the dependence upon t.
p. 434, missing dot product in Equation 16.104
Wave Packets: There have been more queries and complaints about wave packets than any other single topic in the book. I am hoping that with a few extra words, I can help clear up some of the confusion. Comments on whether the extra words help or make things worse are welcome! Click here for extra comments on wave packets (90 kB, pdf) (104 kB, PostScript)
p. 453 In Equation (17.57), the density of electrons n should be replaced by the density of holes p, defined in Equation (17.96).
p. 460 In Equation (17.90) missing vector sign over k.
p. 477 Add a term of the form D \partial f/\partial \mu to the right hand side of Equation (17.190), and neglect a term proportional to \partial^2 f/\partial \mu^2 during the calculation.
p. 492, before Equation (18.35) the source of the tight-binding model is (8.35), not (18.44)
*p. 568, Figure 20.2 is a mirror image of the correct figure.
p. 639, Figure 23.2, y axis label should read “Complex refractive index”
p. 741, Equation (25.157) six final terms on lhs should be multiplied by R.
p. 742, Equation (25.160) third term from left should not have factor of 1/\nu.
p. 763 “could moved about” is “could be moved about”. “becomes more effective in scattering electron” should be “becomes more effective in scattering electrons”
p. 784, Before Equation (27.7), z<0 should be z>0.
p. 785, After Equation (27.9), reference to Equation (27.11) should be reference to Equation 24.3. Equation (27.10), the factor of ½ should follow the sum.
p. 786, Equations (27.11) and (27.12), the subscript on A should be \beta, and the sum should be over \beta only. Equation (27.13), the sum is over \beta.
p. 787, Equation (27.23), first factor of 4\pi should be omitted.
p. 788, Throughout section, interpret m as an effective mass m^\star
p. 789, Equation (27.30); it is the component of this current normal to the boundary that vanishes.
p. 792, Equation (27.44), need extra factor of ½. Equation (27.46), subtract rather than adding last term.
p. 795, to improve consistency with conventions in later sections, reverse the sign on \phi in Equations (27.55) through (27.58).
p. 797, Equation (27.66), missing exponential factor in second term. Reverse the sign on all \phi in (27.65) and (27.66)
p. 799, In Section 27.2.8, replace \Phi_0 / 2 throughout by \Phi_0 / 4\pi , and repair sign conventions in (27.76)
p. 800, in paragraph after (27.78) \gamma_{13} should be \gamma_{23}. Repair sign conventions on all phases in page. In Equation (27.81) missing factor of 8\pi e, and reverse sign of \phi.
p. 808, Equation (27.117) needs overall factor of ½ on right hand side.
p. 811 and 812, Equations (27.133) and (27.140) need additional factors of ½ for four-Fermion terms.
p. 813, Equation (27.145), eliminate factor of 1/N!. Equation (27.148), last c_k^\dag is c_{--k}^\dag.
p. 814, Equation (27.156) on lhs \mu should be \mu N.
p. 815, Equation (27.165), factor of ½ should come outside bracket.
p. 816, Equation (27.173), sum over k', not k.
p. 817, Equation (27.181) and preceding paragraph, order of two Fermion operators should be reversed in all terms. Equation (27.183) third term, replace k by k'. Equation (27.184) sum middle two terms only over k.
p. 819, Equation (27.199) sum on lhs should only be over k'.
p. 820, Equation (27.203) excess U0 in brackets.
p. 821, Equation (27.208), lhs is really H-\mu N. Sum last term over q.
p. 823, Equation (27.219b) replace u by v. In Equation (27.220a&b) reverse sign of \mu.
p. 824, before Equation (27.221a), replace k by k'. Equation (27.224a) \Delta is \Delta^*. Equation (27.227) add rather than subtracting term with A.
p. 831, Equation (27.247), A goes to A +\grad \chi.
p. 836, Equation (27.260), reverse sign on right hand side.
p. 851, formal relation-->formal relations