Redeployment of free electron and DOS notebooks.

Author: Taylor-96

notebook/band-theory/density_of_states.ipynb

@@ -52,7 +52,7 @@
     "    <summary style=\"color: red\">Solution</summary>\n",
     "    In the right panel, the plotted blue line is the analytical result for the DOS of the free electron model. \n",
     "    By choosing different numbers of k-points via the \"Number of k-points slider\", we can investigate how \n",
-    "    the quality of the calculated results varies with the density of the k-point mesh. You will observe that the numerical results converge to the analytical result with increasing number of k-points. This can be attributed to the fact that the DOS can be interpreted as a probability density of electronic states as a function of energy. Since energy is generally related to the k-vector magnitude, the quality with which we resolve the range of energy eigenvalues is in turn directly controlled by how fine our sampling of the k-point mesh is.\n",
+    "    the quality of the calculated results varies with the density of the k-point mesh. You will observe that the numerical results converge to the analytical result with increasing number of k-points. This can be attributed to the fact that the DOS can be interpreted as a probability density of electronic states as a function of energy. Since energy is generally related to the k-vector magnitude, the quality with which we resolve the range of energy eigenvalues is in turn directly controlled by how fine our sampling of the k-point mesh is.  \n",
     "    </details>   \n",
     "\n",
     "2. Which method gives most accurate results? Which method is fastest and why?\n",

notebook/band-theory/free_electron.ipynb

@@ -22,7 +22,7 @@
     "     \n",
     "Throughout the notebook, we employ the empty lattice (free-electron) approximation for the electrons in a periodic \n",
     "solid system.  Using it, we compute and plot the electronic band structure for three \n",
-    "types of Bravais lattice: simple cubic (SC), face-centered cubic (FCC) and body-centered cubic (BCC). We get the path in reciprocal space for the band structure \n",
+    "types of Bravais lattice: simple cubic (SC), face-centered cubic (FCC) and body-centered cubic (BCC). We get the path in reciprocal space for the band structure  \n",
     "from the <a href=\"https://seekpath.readthedocs.io/en/latest/index.html\">seekpath</a>\n",
     "package.\n",
     "\n",
@@ -347,7 +347,7 @@
    "name": "python",
    "nbconvert_exporter": "python",
    "pygments_lexer": "ipython3",
-   "version": "3.10.14"
+   "version": "3.10.12"
   }
  },
  "nbformat": 4,

notebook/band-theory/theory/theory_density_of_states.ipynb

@@ -24,8 +24,7 @@
     "The density of states (DOS) gives a measure of the number of electronic states with values of energy in some interval around a reference value. To be more specific, given a value of electronic energy $E$, the density of states $D(E)$ is defined as $N(E)=D(E)\\delta E$ where $N(E)$ is the number of electronic states with energies falling in the interval $[E,E+\\delta E]$. In the accompanying interactive notebook, we present the density of states (DOS) of the three-dimensional free electron model. The free electron \n",
     "model is a simple way to describe the electrons in metal systems (see the [corresponding notebook](./theory_free_electron.ipynb)). \n",
     "\n",
-    "The Schrödinger\n",
-    "equation of the free electron model can be solved analytically. Furthermore, we \n",
+    "The Schrödinger equation of the free electron model can be solved analytically. Furthermore, we \n",
     "can obtain the analytical solution for the DOS of the free electron model. We\n",
     "demonstrate three different methods which can be employed to calculate the density of\n",
     "states (DOS). The methods are: the simple histogram method, Gaussian smearing, and linear tetrahedron interpolation (\"tetrahedra\" or LTI)."
@@ -146,7 +145,7 @@
    "name": "python",
    "nbconvert_exporter": "python",
    "pygments_lexer": "ipython3",
-   "version": "3.9.12"
+   "version": "3.10.12"
   }
  },
  "nbformat": 4,

notebook/band-theory/theory/theory_free_electron.ipynb

@@ -32,7 +32,7 @@
     "## Empty lattice approximation\n",
     "\n",
     "In the empty lattice approximation, the electrons move \"freely\" in a weak, periodic potential. Electron-electron interactions are neglected.\n",
-    "The eigenfunctions of the Schrödinger equation for free electrons are:\n",
+    "The eigenfunctions of the Schrödinger equation for free electrons are: \n",
     "\n",
     "$$\\large \\psi(\\vec{r}) = e^{i\\vec{k} \\cdot \\vec{r}}$$   \n",
     "\n",
@@ -107,7 +107,7 @@
    "name": "python",
    "nbconvert_exporter": "python",
    "pygments_lexer": "ipython3",
-   "version": "3.10.9"
+   "version": "3.10.12"
   }
  },
  "nbformat": 4,