Appendix J: typos in IK's book

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This page contains the list of misprints discovered so far in Ilya Kuprov's "SPIN: from Basic Symmetries to Quantum Optimal Control".

Location Printed Should be
Page 44, under Eq 2.5
"physical meaning of oscillation frequency"
"physical meaning of frequency"
Page 54, under Eq 2.52
"meV"
"MeV"
Page 123 (Eqs 4.66, 4.69, 4.70), Page 126 (Eqs 4.80, 4.81)
\[l\mathord{\buildrel{\lower3pt\hbox{$\scriptscriptstyle\frown$}} \over n} \]
\[{\rm{l\mathord{\buildrel{\lower3pt\hbox{$\scriptscriptstyle\frown$}} \over n} }}\]
Page 123, Eq 4.69
\[\begin{array}{c} \exp \left( { - i{\bf{\bar H}}T} \right) - \exp \left( { + i{{\bf{H}}_0}T} \right)\exp \left( { - i\left( {{{\bf{H}}_0} + {{\bf{H}}_1}} \right)T} \right)\\ \Downarrow \\ {\bf{\bar H}} - \frac{i}{T}l\mathord{\buildrel{\lower3pt\hbox{$\scriptscriptstyle\frown$}} \over n} \left[ {\exp \left( { + i{{\bf{H}}_0}T} \right)\exp \left( { - i\left( {{{\bf{H}}_0} + {{\bf{H}}_1}} \right)T} \right)} \right] \end{array}\]
\[\begin{array}{c} \exp \left( { - i{\bf{\bar H}}T} \right) = \exp \left( { + i{{\bf{H}}_0}T} \right)\exp \left( { - i\left( {{{\bf{H}}_0} + {{\bf{H}}_1}} \right)T} \right)\\ \Downarrow \\ {\bf{\bar H}} = \frac{i}{T}l\mathord{\buildrel{\lower3pt\hbox{$\scriptscriptstyle\frown$}} \over n} \left[ {\exp \left( { + i{{\bf{H}}_0}T} \right)\exp \left( { - i\left( {{{\bf{H}}_0} + {{\bf{H}}_1}} \right)T} \right)} \right] \end{array}\]
Page 172, Eq 4.248
\(\frac{i\sqrt{3}}{12}\)
\(\frac{i}{6}\)
Page 207, Item 4
rth (two instances)
rth
Page 250, top of Fig 6.2 \[ \downarrow \] \[ \times \]
Page 250, top of Fig 6.2 \[ \to \] \[ - \]
Page 291, under Eq 7.1
"the state of the other spin"
"the state of the other system"
Page 294, under Eq 7.7
"where the ISTs are now indexed by ascending rank l and within ranks by ascending projection number m"
"where the ISTs are now indexed by ascending rank l and within ranks by descending projection number m"
Page 295, Eq 7.9
\[\begin{array}{c} {c_{ijk}} = {\rm{Tr}}\left[ {\left( {\mathop \otimes \limits_{n = 1}^N {{\bf{T}}_{l_n^{\left( i \right)}m_n^{\left( i \right)}}}} \right)\left( {\mathop \otimes \limits_{n = 1}^N {{\bf{T}}_{l_n^{\left( j \right)}m_n^{\left( j \right)}}}} \right){{\left( {\mathop \otimes \limits_{n = 1}^N {{\bf{T}}_{l_n^{\left( k \right)}m_n^{\left( k \right)}}}} \right)}^\dagger }} \right] = \\ = {\rm{Tr}}\left[ {\mathop \otimes \limits_{n = 1}^N \left( {{{\bf{T}}_{l_n^{\left( i \right)}m_n^{\left( i \right)}}}{{\bf{T}}_{l_n^{\left( j \right)}m_n^{\left( j \right)}}}{\bf{T}}_{l_n^{\left( k \right)}m_n^{\left( k \right)}}^\dagger } \right)} \right] = \prod\limits_{n = 1}^N {{\rm{Tr}}\left( {{{\bf{T}}_{l_n^{\left( i \right)}m_n^{\left( i \right)}}}{{\bf{T}}_{l_n^{\left( j \right)}m_n^{\left( j \right)}}}{\bf{T}}_{l_n^{\left( k \right)}m_n^{\left( k \right)}}^\dagger } \right)} = \prod\limits_{n = 1}^N {f_{ijk}^{\left( n \right)}} \end{array}\]
\[\begin{array}{c} {\rm{Tr}}\left[ {\left( {\mathop \otimes \limits_{n = 1}^N {{\bf{T}}_{l_n^{\left( i \right)}m_n^{\left( i \right)}}}} \right)\left( {\mathop \otimes \limits_{n = 1}^N {{\bf{T}}_{l_n^{\left( j \right)}m_n^{\left( j \right)}}}} \right){{\left( {\mathop \otimes \limits_{n = 1}^N {{\bf{T}}_{l_n^{\left( k \right)}m_n^{\left( k \right)}}}} \right)}^\dagger }} \right] = \\ = {\rm{Tr}}\left[ {\mathop \otimes \limits_{n = 1}^N \left( {{{\bf{T}}_{l_n^{\left( i \right)}m_n^{\left( i \right)}}}{{\bf{T}}_{l_n^{\left( j \right)}m_n^{\left( j \right)}}}{\bf{T}}_{l_n^{\left( k \right)}m_n^{\left( k \right)}}^\dagger } \right)} \right] = \prod\limits_{n = 1}^N {{\rm{Tr}}\left( {{{\bf{T}}_{l_n^{\left( i \right)}m_n^{\left( i \right)}}}{{\bf{T}}_{l_n^{\left( j \right)}m_n^{\left( j \right)}}}{\bf{T}}_{l_n^{\left( k \right)}m_n^{\left( k \right)}}^\dagger } \right)} \end{array}\]
Page 295, under Eq 7.9
"in terms of the structure coefficients \(f_{ijk}\) of"
"in terms of the structure coefficients of"
Page 295, above Eq 7.10
"given incomplete basis"
"given orthogonal basis"
Page 295, under Eq 7.14
\[{c_{ijk}} = {\rm{Tr}}\left( {{{\bf{O}}_i}{{\bf{O}}_j}{\bf{O}}_k^\dagger } \right)\]
\[{c_{ijk}} = \frac{{{\rm{Tr}}\left( {{{\bf{O}}_i}{{\bf{O}}_j}{\bf{O}}_k^\dagger } \right)}}{{{\rm{Tr}}\left( {{{\bf{O}}_k}{\bf{O}}_k^\dagger } \right)}}\]
Page 296, above Eq 7.17
kth
kth
Page 296, Eq 7.18
\[{\left[ {H_n^{\left( {\rm{L}} \right)}} \right]_{jk}} = \left\langle {{{\bf{O}}_j}} \right|H_n^{\left( {\rm{L}} \right)}\left| {{{\bf{O}}_k}} \right\rangle = {\rm{Tr}}\left( {{\bf{O}}_j^\dagger {{\bf{H}}_n}{{\bf{O}}_k}} \right) = \ldots = {\omega _n}\prod\limits_{m = 1}^N {{\rm{Tr}}\left( {{\bf{S}}_{j,m}^\dagger {{\bf{S}}_{n,m}}{{\bf{S}}_{k,m}}} \right)} \]
\(\begin{matrix} {{\left[ H_{n}^{\left( \text{L} \right)} \right]}_{jk}}=\frac{\left\langle {{\mathbf{O}}_{j}} \right|H_{n}^{\left( \text{L} \right)}\left| {{\mathbf{O}}_{k}} \right\rangle }{\sqrt{\text{Tr}\left( \mathbf{O}_{j}^{\dagger }{{\mathbf{O}}_{j}} \right)}\sqrt{\text{Tr}\left( \mathbf{O}_{k}^{\dagger }{{\mathbf{O}}_{k}} \right)}}= \\ \frac{\text{Tr}\left( \mathbf{O}_{j}^{\dagger }{{\mathbf{H}}_{n}}{{\mathbf{O}}_{k}} \right)}{\sqrt{\text{Tr}\left( \mathbf{O}_{j}^{\dagger }{{\mathbf{O}}_{j}} \right)}\sqrt{\text{Tr}\left( \mathbf{O}_{k}^{\dagger }{{\mathbf{O}}_{k}} \right)}}=\ldots ={{\omega }_{n}}\prod\limits_{m=1}^{N}{\frac{\text{Tr}\left( \mathbf{S}_{j,m}^{\dagger }{{\mathbf{S}}_{n,m}}{{\mathbf{S}}_{k,m}} \right)}{\sqrt{\text{Tr}\left( \mathbf{S}_{j,m}^{\dagger }{{\mathbf{S}}_{j,m}} \right)}\sqrt{\text{Tr}\left( \mathbf{S}_{k,m}^{\dagger }{{\mathbf{S}}_{k,m}} \right)}}} \end{matrix}\)
Page 362, Eq 9.16
\[\left[ math \right]\]
\[ math \]