kkrimp/theory.md

@@ -5,8 +5,8 @@ background of the impurity calculations. To find more details on the
 theory and a detailed description on the method follow the following
 links:
 
- * PhD thesis of D. Bauer (https://publications.rwth-aachen.de/record/229375)
- * Dederichs et al., MRS Proceedings 253, 185 (1991)
+  * PhD thesis of D. Bauer (https://publications.rwth-aachen.de/record/229375)
+  * Dederichs et al., MRS Proceedings 253, 185 (1991)
 
 ## Green function based DFT calculations
 
@@ -108,12 +108,12 @@ and the latter multiple-scattering or backscattering contribution.
 To calculate the impurity Green function we make use of the Dyson
 equation. The idea is that an impurity locally changes the potential.
 This perturbation extends only over a small area that typically
-containes the impurity and the first few shells of neighbors. Then
+contains the impurity and the first few shells of neighbors. Then
 outside this impurity region the potentials do not change any more and
-consequently the difference in the single-site $t$-matrices of these
+consequently the difference in the single-site $`t`$-matrices of these
 positions vanish, i.e. $`\Delta t=0`$. This allows us to embed the
 impurity in a finite real space cluster into the host system. The
-calcualtion is then done as follows.
+calculation is then done as follows.
 
  - Compute the host systems Green function and write out the structural Green function as well as the single-site $`t`$ matrix of the host $`t_{\mathrm{host}}`$.
  - From the impurity potential compute the $t$-matrix of the impurity and construct $`\Delta t=t_{\mathrm{host}}-t_{\mathrm{imp}}`$