pre-rewrite: some small typo fixes

roam/data/d6/e44fbc-975b-463d-87f9-878d50758b55/index.tex

@@ -883,7 +883,7 @@ For \(n>m\) we have
   Δ_{+,-}&=2δ\\
   \label{eq:57}Δ_{n>0,-} &= n Ω_{B} + δ\\
   \label{eq:58}Δ_{n>0,+} &= n Ω_{B} - δ\\
-  \label{eq:59}Δ_{n>0,m>0} &= (n-m) Ω_{B} - δ.
+  \label{eq:59}Δ_{n>0,m>0} &= (n-m) Ω_{B}.
 \end{align}
 To couple exactly one other mode with \(n>0\) to the \(+\) mode, the
 RWA requires that \(\abs{Δ_{n,+}}\neq \abs{Δ_{kl}}\) for \(k\neq n\), \(l\neq +\).
@@ -1009,7 +1009,7 @@ With this, we have for \(m=\pm,-N,-N+1,\ldots,-1,1,2,\ldots,N\)
 \begin{equation}
   \label{eq:94}
   \begin{aligned}
-    ω^{0}_{m\neq \pm} &= ω_{n}^{B} & ω^{0}_{\pm} &= \pm δ \cos(ψ)\\
+    ω^{0}_{m\neq \pm} &= ω_{n}^{B} & ω^{0}_{\pm} &= ω_{s} \pm δ \cos(ψ)\\
     η^{0}_{m\neq\pm} &= η_{B} = η_S+2δΔ & η^{0}_{\pm} &=  η_{S} + δΔ =
                                                       \frac{η_{S}+ η_{B}}{2}.
   \end{aligned}