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lines changed Original file line number Diff line number Diff line change @@ -970,9 +970,9 @@ <h2 id="rewriting-the-string-of-matrices" class="anchor">Rewriting the string of
970970< p > Use the commutation relations of the Pauli matrices to reorder the string. The commutation relations are:</ p >
971971$$
972972[\sigma_i, \sigma_j] = 2i \epsilon_{ijk} \sigma_k,
973- \]
974- where $\epsilon_{ijk}$ is the Levi-Civita symbol. This allows you to move certain Pauli matrices to the left or right in the string.
975973$$
974+
975+ < p > where \( \epsilon_{ijk} \) is the Levi-Civita symbol. This allows you to move certain Pauli matrices to the left or right in the string.</ p >
976976</ div >
977977</ div >
978978
Original file line number Diff line number Diff line change @@ -800,22 +800,24 @@ <h2 id="rewriting-the-string-of-matrices">Rewriting the string of matrices </h2>
800800< b > Commute and reorder:</ b >
801801< p >
802802< p > Use the commutation relations of the Pauli matrices to reorder the string. The commutation relations are:</ p >
803+ < p > < br >
803804$$
804805[\sigma_i, \sigma_j] = 2i \epsilon_{ijk} \sigma_k,
805- \]
806- where $\epsilon_{ijk}$ is the Levi-Civita symbol. This allows you to move certain Pauli matrices to the left or right in the string.
807- < p > < br >
808806$$
807+ < p > < br >
808+
809+ < p > where \( \epsilon_{ijk} \) is the Levi-Civita symbol. This allows you to move certain Pauli matrices to the left or right in the string.</ p >
809810</ div >
810811
811812< div class ="alert alert-block alert-block alert-text-normal ">
812813< b > Simplify using identities:</ b >
813814< p >
814815< p > Use the fact that \( \sigma_i^2 = I \) and \( \sigma_i \sigma_j = -\sigma_j \sigma_i \) for \( i \neq j \) to simplify the expression. For example:</ p >
815- $$
816816< p > < br >
817+ $$
817818\boldsymbol{X} \boldsymbol{Y} = -\boldsymbol{Y} \boldsymbol{X} = i \boldsymbol{X}.
818819$$
820+ < p > < br >
819821</ div >
820822</ section >
821823
Original file line number Diff line number Diff line change @@ -892,9 +892,9 @@ <h2 id="rewriting-the-string-of-matrices">Rewriting the string of matrices </h2>
892892< p > Use the commutation relations of the Pauli matrices to reorder the string. The commutation relations are:</ p >
893893$$
894894[\sigma_i, \sigma_j] = 2i \epsilon_{ijk} \sigma_k,
895- \]
896- where $\epsilon_{ijk}$ is the Levi-Civita symbol. This allows you to move certain Pauli matrices to the left or right in the string.
897895$$
896+
897+ < p > where \( \epsilon_{ijk} \) is the Levi-Civita symbol. This allows you to move certain Pauli matrices to the left or right in the string.</ p >
898898</ div >
899899
900900< div class ="alert alert-block alert-block alert-text-normal ">
Original file line number Diff line number Diff line change @@ -969,9 +969,9 @@ <h2 id="rewriting-the-string-of-matrices">Rewriting the string of matrices </h2>
969969< p > Use the commutation relations of the Pauli matrices to reorder the string. The commutation relations are:</ p >
970970$$
971971[\sigma_i, \sigma_j] = 2i \epsilon_{ijk} \sigma_k,
972- \]
973- where $\epsilon_{ijk}$ is the Levi-Civita symbol. This allows you to move certain Pauli matrices to the left or right in the string.
974972$$
973+
974+ < p > where \( \epsilon_{ijk} \) is the Levi-Civita symbol. This allows you to move certain Pauli matrices to the left or right in the string.</ p >
975975</ div >
976976
977977< div class ="alert alert-block alert-block alert-text-normal ">
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