List of (Suspected) Errata and Formatting Issues

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Important Remarks

Since the actual LaTeX commands are hard to guess, they may be transcribed, abbreviated or imagined.
The following scheme is used:
description of the location of the issue: description of the issue
Which you can write like in this example:

- [ ] on p. 123 in (45): missing `i` in `\exp`

which would look like this:

on p. 123 in (45): missing i in \exp
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List of contributors

Peter
Margarit
Jens

List of (Suspected) Errata, Formatting Issues & Suggestions for the PMI script (2020/21)

General Remarks

It would be nice, if all equations were numbered, making referring to them easier.
When referencing back to definitions from previous chapers it would be helpful to add a \eqref to the corresponding equation (e.g. when \hat{\bar{H}} is referenced in chapter 8.2`). This makes it also easier to understand when a symbol is to be understood in its most general or approximated version. (At the beginning of chapter 8.2.2 this is done nicely for the CI matrix.)

By Section

1 (downloaded 2.9.2020)

2 (downloaded 2.9.2020)

after (6): (??) looks like a corrupted \eqref

3 (downloaded 11.9.2020)

(46): missing \perp symbol in delta-dyadic
(58): formatting of velocity off (wrong order of _ and \vec suspected)
p.32 last equation last line: missing 2 before \vec{A}^2

4 (downloaded 15.9.2020)

mode expansion, before (79) & after (81) (pp 37+38) in normalization factor (occurs multiple times over the script): should be V not \sqrt
after (80): 2x missing ), missing index in momenta in commutator, \vec{\Pi} used instead of \hat{\Pi}
(81): \vec{\Pi} used instead of \hat{\Pi}
(81): missing \perp on delta dyadic, the vanishing grad of delta^\perp was already shown in sec. 1

5 (downloaded 17.9.2020)

after 5.1 heading: 2x missing )
(87): order of operators wrong on the right side of the second equation
after (87) in matrix element of exp(i \phi) and also later: first Kronecker delta should be \delta_{n,0} (not with an m) and even better \delta{m, n-1} for the entire matrix element (much simpler and easier to the the hermitian property of cos/sin(\phi) later on)
matrix element of sin(\phi) (occurs multiple times over the script): missing factor 1/i

5.2 (downloaded 17.9.2020)

in [n, exp(i\phi)]: one \hat{a} too many in the middle & missing minus (-) sign in the last expression
(89) and also before that: missing n in \ket
(89): missing i in 2nd exponent
(90) 2nd line: there should not be a + \hat{a}^\dagger

5.3 (downloaded 19.9.2020)

after (98) in <\alpha|\beta>: |\beta|^2 should be in the numerator (not denominator)
after (99) 2nd line in completeness relation proof: wrong order of \bra <-> \ket

5.4 (downloaded 19.9.2020)

(100): remove the 1/2 in front of t factor in exponential inside the sum
after (100) 2nd line: remove one )
after (100) 3rd line: \sum should be over m
after (101) on page 55 2nd line: missing i in expansion of \cos
after (101) on page 55 5th line: missing i in exp (which becomes \cos)
after (101) on page 55 5th line: missing \infinity above sum
(102): redundant \eq (=) sign

6 (downloaded 19.9.2020)

(105): missing \alpha in front of sum

7 (downloaded 22.9.2020)

way after (106) on p. 66 after definition of order of 1st coherence function, the trivial clause: there should not be primed coordinates i.e.g^{(1)}(x,t,x,t).
after definition of second-order field correlation function: should be G^{(2)}(x_1,t_1,x_2,t_2,x_1,t_1,x_2,t_2) \geq 0 (and not ...x_3,t_3,x_4,t_4)
p. 68 example (a) 2nd line: |n should be inside ket
p. 68 example (b) 2nd line: square should be in the denominator (not numerator)

8/8.1.1 (downloaded 25.9.2020)

8.1.2 (downloaded 25.9.2020)

8.1.3 (downloaded 25.9.2020)

p.79 listed item 2. middle of the line: missing \Rightarrow
p.79 item 3. 3rd line: missing \hat{c}^\dagger_p on the right side
p.79 item 5. 1st sentence: typo of of
p.80 item 8. 2nd line: missing \hat{c}_p
p.80 item 8. 3rd line lower branch of curly braces: inconsistency in space placement, put space after ,

8.2 (dowloaded 2.12.20)

p.82 first equation ket on the right: sould be a \ket{ \{n_p\} } (not \psi)
p.82 last paragraph: typo for a one-body operators
(suggestion) p.83 1st paragraph: In general, use the notation \vec{n} and \vec{n^\prime} instead of \{n_p\} and \{n_q\} to denote occupation numbers. This will avoid confusion in expressions like n_r = 1. Alternatively, more specific and use expressions like n_{p,r} = 1 instead.
(suggestion) p.83 1st paragraph last sentence: mention indices of orbitals s and r explicitly.
(suggestion) p.84 last equation 1st line: maybe explain the meaning of \epsilon_i here (it was not obvious that it is from \hat{\bar{H}} which includes the + \hat{\bar{V}} and thus the + \sum_i\bar{V}_{ii} arises later).

8.3 (downloaded 2.12.2020)

8.7

p.106 top: typo Hatree-Salter
p.106 end of this section: unfinished sentence

8.8

9.1

p.114 last equation 2nd line: missing \dagger
p.115 last equation last line: missing prefactor of 2 (?)
p.115 last equation last line: missing i in \exp

9.2

(suggestion) p. 118 (129: It would be nice, if the notation style is consistent with the previous chapters, i.e. if the sub-- and superscripts N_{el} and 0 were place inside the ket.
p.119 after (130): missing restriction in higher order integral t^prime \leq t
(suggestion) p.119 end: Mention that up to 1st order this result for the transition rate is also known as Fermi's golden rule. This makes it easier to find secondary literature.
p.119 2nd equation 2nd line: m should be M
(suggestion) p.119 2nd equation: The justification for dropped terms with \epsilon is not obvious and is therefore confusing - it also violates the strict meaning of the equals sign. It would be good to give an explanation here.

9.3

p.120 1st equation:l not in index, should be N__{el}
p.120 2nd equation 1st line: remove - in front of N_{el}}
(suggestion)p.121 dipole approx: Maybe be more explicit about the approximation, i.e. mention that \abs{\vec{k}_{in} \vec{x}} \ll 1 and therefore the wavelength of the photon must be large.
p.120 dipole approx.: The connection from hat{\vec{p}}} to \hat{\vec{r}} as the perturbation operator is missing. See e.g. here. Note: This is a simple yet important derivation and it was crucial when we found a mistake in the numerical exercises.
p.120: typo singl-mode
p.120 2nd equation 1st line: remove minus in front of N_{el} in \bra{\Psi_F^{-N_{el}}}
p.121 2nd paragraph: typo ev instead of eV

9.4

p.122 1st equation: missing index in for \vec{k} in the \exp(i k x)-term
p.122 1st paragraph: typo on-photon
p.123 before the exercise: typo integrating of better: over
p.126 1st equation 2nd to last line: missing \tilde on q in E_q^{3/2} in numerator
(suggestion) p.125-126: The notation for the free electron momentum q is inconsistent and confusing: The angular wheight d \Omega_{\vec{q}} for example has no \tilde but the final momentum \tilde{\vec{q}} does. It seems simpler to drop the index in d \Omega and give the momentum q while it is in the kernel pf the integral a \prime or something similar.

10.1

p.136 1st equation: \gamma should be \theta
p.137 2nd equation: \exp (i \vec{x}\vec{x}) should be \exp (i \vec{k} \vec{x}
p.137 1st, 5th, 6th eauqtion: inconsistency of the symbol for the principal quantum number, previously \xi now \epsilon, (this migth appear multiple times thoughout the script)

11.1

p.139 2nd equation: nontaion of final state in incinsistent F and f
p.148 in paragraph after last equation: N should be n in \bra{\Psi_N^{N_{el}-1}}
p.151 caption of figure 16 and 17: typo Satnra
p.151 aption of figure 17: typo Koopman'stheorem

12

p.152 after 1st equation: \Lambda_{in} should be \lambda_{in}
p.152 last equation last line: missing \sum \limits_{p,q}
p.153 3rd equation: missing i in \exp
p.156 last block of eqautions 1st line: missing ^3 shortly after \Rightarrow`
p.156 1st equation last line: 1_s sould b3e 1s`

13

p.165 last equation: ,L_{2,3} should be in index
p.156 after figure 19: typo that mediated

14

p.169 first paragraph: equation reference still incomplete

15

p.177 1st equation line 3 first bra: missing -1
p.178 1st equation last line in denominator: i \epsilon should not be in superscript
p.177 1st equation last line in first ket: turn index p into q
p.177 1st equation last line in last ket: turn index q into q^\prime

15.1

p.180 1st equation last polarization vector: missplaced conjugation symbol

15.2

p.186: typo a t
p.186 2nd equation 2nd line: missing summation index
p.188 last equation 4th line: sign in front of \omega_{in} should be negative
p.188 last equation last line: missing ^3 in big O
p.190 typo: differenctial

16

p.193 eq. 156: inconsistency: photon state should be on the left
p.193 eq. 156: typo remove ; and ,
p.195 middle of page: typo \Omega_F should be \omega_F
p.196 2nd equation 2nd line: rightmost fraction should be polarization sum
p.196 3rd equation 1st line: = should be \approx
p.196 3rd equation 2nd line rightmost term: misplaced \tilde on \omega_F
p.196 4th equation: missing \sum
p.197 typo: missing \ in front of sigma_{0,F}

Edited Apr 15, 2021 by Lucas Kemmler

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