X-Git-Url: https://hackdaworld.org/gitweb/?p=lectures%2Flatex.git;a=blobdiff_plain;f=physics_compact%2Fsolid.tex;fp=physics_compact%2Fsolid.tex;h=bc70eaea8e7b940fd87783d7e5cd412afaef5392;hp=5e69a799a18a5174921aabe05797cc83202675e6;hb=4533f8a3f2d7319103d979de2255a43ba2cb9235;hpb=6a26b9f5593acc0bf19241b2fe79f1acf51fb03e

diff --git a/physics_compact/solid.tex b/physics_compact/solid.tex
index 5e69a79..bc70eae 100644
--- a/physics_compact/solid.tex
+++ b/physics_compact/solid.tex
@@ -282,18 +282,26 @@ The contributions of this operator act differently on $\ket{l,m}$ and --- in fac
 L_+S_-\ket{l,m,+}=L_+\ket{l,m}S_-\ket{+}=
 \sqrt{(l-m)(l+m+1)}\hbar\ket{l,m+1}\hbar\ket{-}
 \end{equation}
+      Moreover, this part only acts on magnetic quantum numbers
+      $m=-l,\ldots,l-1$ and updates quantum numbers $m=-l+1,\ldots,l$.
 \item \underline{$L_-S_+$}:
       Updates spin up component and only acts on spin down component
 \begin{equation}
-L_+S_-\ket{l,m,-}=L_+\ket{l,m}S_-\ket{+}=
-\sqrt{(l-m)(l+m+1)}\hbar\ket{l,m+1}\hbar\ket{-}
+L_-S_+\ket{l,m,-}=L_+\ket{l,m}S_+\ket{-}=
+\sqrt{(l+m)(l-m+1)}\hbar\ket{l,m-1}\hbar\ket{+}
 \end{equation}
+      Moreover, this part only acts on magnetic quantum numbers
+      $m=-l+1,\ldots,l$ and updates quantum numbers $m=-l,\ldots,l-1$.
 \item \underline{$L_zS_z$}: Acts on both and updates both spinor components
 \begin{equation}
 L_zS_z\ket{l,m,\pm}=L_z\ket{l,m}S_z\ket{\pm}=
 \pm\frac{1}{2}m\hbar^2\ket{l,m,\pm}
 \end{equation}
+      It acts on all magnetic quantum numbers and updates all of them.
 \end{enumerate}
+Please note that the $\ket{l,m,\pm}$ are not eigenfunctions of the two combinations of ladder operators, i.e.\  the $\ket{l,m,\pm}$ do not diagonalize the spin-orbit part of the Hamiltonian.
+(Does this constitute a problem?)
+
 
 \subsubsection{Excursus: Real space representation within an iterative treatment}