diff --git a/notebook/lattice-vibration/Molecule_Vibration.ipynb b/notebook/lattice-vibration/Molecule_Vibration.ipynb
index 44fa107..e91b7c4 100644
--- a/notebook/lattice-vibration/Molecule_Vibration.ipynb
+++ b/notebook/lattice-vibration/Molecule_Vibration.ipynb
@@ -10,7 +10,7 @@
     "\n",
     "<i class=\"fa fa-home fa-2x\"></i><a href=\"../index.ipynb\" style=\"font-size: 20px\"> Go back to index</a>\n",
     "\n",
-    "**Source code:** https://github.com/osscar-org/quantum-mechanics/blob/develop/notebook/lattice-vibration/Molecule_Vibration.ipynb\n",
+    "**Source code:** https://github.com/osscar-org/quantum-mechanics/blob/master/notebook/lattice-vibration/Molecule_Vibration.ipynb\n",
     "\n",
     "\n",
     "With this notebook, the concept of molecular vibration is explored and visualized in an interactive fashion.\n",
@@ -338,7 +338,7 @@
    "name": "python",
    "nbconvert_exporter": "python",
    "pygments_lexer": "ipython3",
-   "version": "3.9.12"
+   "version": "3.10.12"
   }
  },
  "nbformat": 4,
diff --git a/notebook/lattice-vibration/NGLTrajectoryClass2D.py b/notebook/lattice-vibration/NGLTrajectoryClass2D.py
index 4dccdd9..bb70b9d 100644
--- a/notebook/lattice-vibration/NGLTrajectoryClass2D.py
+++ b/notebook/lattice-vibration/NGLTrajectoryClass2D.py
@@ -162,10 +162,16 @@ def __init__(self, trajectory):
         self.kx_array = np.linspace(-1.5 * np.pi, 1.5 * np.pi, 61)
         self.ky_array = np.linspace(-1.5 * np.pi, 1.5 * np.pi, 61)
         self.KX, self.KY = np.meshgrid(self.kx_array, self.ky_array)
-        # Center of Brillouin zone
-        self.idx_x = 30
-        self.idx_y = 30
+        
+        # Initialize to nontrivial k-point
+        self.x=np.pi/2
+        self.y=np.pi/2
+        self.idx_x = (np.abs(self.kx_array - self.x)).argmin()
+        self.idx_y = (np.abs(self.ky_array - self.y)).argmin()
 
+        kx = self.kx_array[self.idx_x]
+        ky = self.ky_array[self.idx_y]
+       
 
         # kx,ky bounds are 1.5*BZ edge
         self.kx_array_honey = np.linspace(-1.5 * 2 * np.pi / 3, 1.5 * 2 * np.pi / 3, 61)
@@ -176,8 +182,8 @@ def __init__(self, trajectory):
         self.KX_honey, self.KY_honey = np.meshgrid(
             self.kx_array_honey, self.ky_array_honey
         )
-        self.idx_x_honey = 30
-        self.idx_y_honey = 30
+        self.idx_x_honey = 50
+        self.idx_y_honey = 50
 
         # View settings
         self.init_delay = 20
@@ -498,7 +504,15 @@ def initialize_2D_band_plot(self):
         self.ax.set_yticks(np.linspace(-np.pi, np.pi, 5))
         self.ax.set_yticklabels(["$-\pi/a$", "", "0", "", "$\pi/a$"])
 
-        (self.point,) = self.ax.plot([0], [0], ".", c="crimson", markersize=10)
+        
+        self.x=np.pi/2
+        self.y=np.pi/2
+        self.idx_x = (np.abs(self.kx_array - self.x)).argmin()
+        self.idx_y = (np.abs(self.ky_array - self.y)).argmin()
+
+        kx = self.kx_array[self.idx_x]
+        ky = self.ky_array[self.idx_y]
+        (self.point,) = self.ax.plot([kx], [ky], ".", c="crimson", markersize=10) # TODO CHANGE INITIAL MARKER POS
 
         self.fig.canvas.mpl_connect("button_press_event", self.onclick)
         plt.ion()
@@ -544,7 +558,20 @@ def initialize_paths_bands(self):
         self.ax_.plot([20, 20], [0, 10000], "k--")
         self.ax_.plot([40, 40], [0, 10000], "k--")
 
-        (self.point_,) = self.ax_.plot([], [], "r.", markersize=10)
+                
+        self.x=np.pi/2
+        self.y=np.pi/2
+        self.idx_x = (np.abs(self.kx_array - self.x)).argmin()
+        self.idx_y = (np.abs(self.ky_array - self.y)).argmin()
+
+        kx = self.kx_array[self.idx_x]
+        ky = self.ky_array[self.idx_y]
+        
+        # default chosen to be on gamma-M
+        idx = np.where(np.all([kx, ky] == np.c_[self.kx_GM, self.ky_GM], axis=1))[
+                0
+            ][0]
+        (self.point_,) = self.ax_.plot([idx], [self.w_long[self.idx_x][self.idx_y]], "r.", markersize=10)
 
         # Position of the high symmetry points
         self.ax_.set_xticks([0, 20, 40, 60])
diff --git a/notebook/lattice-vibration/NGLUtilsClass.py b/notebook/lattice-vibration/NGLUtilsClass.py
index 6498d20..243c7c7 100644
--- a/notebook/lattice-vibration/NGLUtilsClass.py
+++ b/notebook/lattice-vibration/NGLUtilsClass.py
@@ -95,7 +95,7 @@ def __init__(self, trajectory) -> None:
             r"Arrow amplitude", layout=self.layout_description
         )
         self.slider_amp_arrow = widgets.FloatSlider(
-            value=0.5,
+            value=2.0,
             min=0.1,
             max=5.01,
             step=0.1,
diff --git a/notebook/lattice-vibration/Phonon_2D.ipynb b/notebook/lattice-vibration/Phonon_2D.ipynb
index a929280..04b8f4f 100644
--- a/notebook/lattice-vibration/Phonon_2D.ipynb
+++ b/notebook/lattice-vibration/Phonon_2D.ipynb
@@ -10,7 +10,7 @@
     "\n",
     "<i class=\"fa fa-home fa-2x\"></i><a href=\"../index.ipynb\" style=\"font-size: 20px\"> Go back to index</a>\n",
     "\n",
-    "**Source code:** https://github.com/osscar-org/quantum-mechanics/blob/develop/notebook/lattice-vibration/Phonon_2D.ipynb\n",
+    "**Source code:** https://github.com/osscar-org/quantum-mechanics/blob/master/notebook/lattice-vibration/Phonon_2D.ipynb\n",
     "\n",
     "This notebook extends the notion of phonons to the 2D case. In this notebook, the link between the reciprocal space and the band dispersion plot along certain path is made explicit. The wave can now be transversal as opposed to longitudinal only in the 1D phonon case. A simple example, the square lattice, and a more complex one, the honeycomb lattice, are presented.\n",
     "<hr style=\"height:1px;border:none;color:#cccccc;background-color:#cccccc;\" />"
@@ -27,6 +27,14 @@
     "* Discover the importance of highly symmetrical points."
    ]
   },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "## **Background theory** \n",
+    "[More on the background theory.](./theory/theory_phonon_2d.ipynb)"
+   ]
+  },
   {
    "cell_type": "markdown",
    "metadata": {},
@@ -100,7 +108,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": null,
+   "execution_count": 7,
    "metadata": {},
    "outputs": [],
    "source": [
@@ -122,7 +130,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": null,
+   "execution_count": 8,
    "metadata": {},
    "outputs": [],
    "source": [
@@ -135,7 +143,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": null,
+   "execution_count": 9,
    "metadata": {},
    "outputs": [],
    "source": [
@@ -149,7 +157,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": null,
+   "execution_count": 10,
    "metadata": {},
    "outputs": [],
    "source": [
@@ -186,10 +194,14 @@
     "for widget in widgets:\n",
     "    handler.widgetList.append(widget)\n",
     "\n",
-    "handler.tick_box_arrows.value = False\n",
+    "handler.slider_atom_radius.value=0.1\n",
+    "handler.slider_arrow_radius.value=0.05\n",
+    "handler.tick_box_arrows.value=True\n",
+    "handler.addArrows() # add arrows by default\n",
+    "\n",
+    "handler.tick_box_arrows.value = True\n",
     "handler.set_view_parameters(clipDist=1, quality=\"low\")\n",
     "# handler.slider_atom_radius.value = 0.1\n",
-    "handler.slider_arrow_radius.value = 0.1\n",
     "handler.set_player_parameters(delay=handler.init_delay)\n",
     "handler.set_view_dimensions()\n",
     "handler.button_lattice.observe(on_lattice_change,\"value\")\n",
@@ -335,9 +347,26 @@
   },
   {
    "cell_type": "code",
-   "execution_count": null,
+   "execution_count": 11,
    "metadata": {},
-   "outputs": [],
+   "outputs": [
+    {
+     "data": {
+      "text/html": [
+       "<style>\n",
+       ".box_style{\n",
+       "    border : 2px solid red;\n",
+       "}\n",
+       "</style>\n"
+      ],
+      "text/plain": [
+       "<IPython.core.display.HTML object>"
+      ]
+     },
+     "metadata": {},
+     "output_type": "display_data"
+    }
+   ],
    "source": [
     "%%html\n",
     "<style>\n",
@@ -349,9 +378,38 @@
   },
   {
    "cell_type": "code",
-   "execution_count": null,
+   "execution_count": 12,
    "metadata": {},
-   "outputs": [],
+   "outputs": [
+    {
+     "data": {
+      "application/vnd.jupyter.widget-view+json": {
+       "model_id": "392bd39bbb0845409a9b73607dd2b574",
+       "version_major": 2,
+       "version_minor": 0
+      },
+      "text/plain": [
+       "VBox(children=(Tab(children=(VBox(children=(GridBox(children=(VBox(children=(Output(),), layout=Layout(grid_ar…"
+      ]
+     },
+     "metadata": {},
+     "output_type": "display_data"
+    },
+    {
+     "data": {
+      "application/vnd.jupyter.widget-view+json": {
+       "model_id": "b58c1354d9a443aebd43315215a2ec1e",
+       "version_major": 2,
+       "version_minor": 0
+      },
+      "text/plain": [
+       "HBox(children=(NGLWidget(max_frame=60),), layout=Layout(align_items='center', display='flex', flex_flow='colum…"
+      ]
+     },
+     "metadata": {},
+     "output_type": "display_data"
+    }
+   ],
    "source": [
     "display(actions, HBox([handler.view], layout=layout).add_class(\"box_style\"))"
    ]
@@ -425,7 +483,7 @@
    "name": "python",
    "nbconvert_exporter": "python",
    "pygments_lexer": "ipython3",
-   "version": "3.9.12"
+   "version": "3.10.12"
   }
  },
  "nbformat": 4,
diff --git a/notebook/lattice-vibration/theory/theory_molecular_vibration.ipynb b/notebook/lattice-vibration/theory/theory_molecular_vibration.ipynb
index 7acee06..5852fa3 100644
--- a/notebook/lattice-vibration/theory/theory_molecular_vibration.ipynb
+++ b/notebook/lattice-vibration/theory/theory_molecular_vibration.ipynb
@@ -5,6 +5,7 @@
    "metadata": {},
    "source": [
     "# **Background theory**: Introduction to molecular vibrations\n",
+    "\n",
     "<i class=\"fa fa-book fa-2x\"></i><a href=\"../Molecule_Vibration.ipynb\" style=\"font-size: 20px\"> Go back to the interactive notebook</a>\n",
     "\n",
     "**Source code:** https://github.com/osscar-org/quantum-mechanics/tree/develop/notebook/lattice-vibration/theory/theory_molecular_vibration.ipynb\n",
@@ -19,7 +20,11 @@
    "outputs": [
     {
      "data": {
-      "application/javascript": "MathJax.Hub.Config({\n    TeX: { equationNumbers: { autoNumber: \"AMS\" } }\n});\n",
+      "application/javascript": [
+       "MathJax.Hub.Config({\n",
+       "    TeX: { equationNumbers: { autoNumber: \"AMS\" } }\n",
+       "});\n"
+      ],
       "text/plain": [
        "<IPython.core.display.Javascript object>"
       ]
@@ -158,9 +163,9 @@
    "name": "python",
    "nbconvert_exporter": "python",
    "pygments_lexer": "ipython3",
-   "version": "3.8.10"
+   "version": "3.10.12"
   }
  },
  "nbformat": 4,
- "nbformat_minor": 2
+ "nbformat_minor": 4
 }
diff --git a/notebook/lattice-vibration/theory/theory_phonon_1d.ipynb b/notebook/lattice-vibration/theory/theory_phonon_1d.ipynb
index c5e41ab..19b73e3 100644
--- a/notebook/lattice-vibration/theory/theory_phonon_1d.ipynb
+++ b/notebook/lattice-vibration/theory/theory_phonon_1d.ipynb
@@ -14,29 +14,14 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 16,
+   "execution_count": 3,
    "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "application/javascript": [
-       "MathJax.Hub.Config({\n",
-       "    TeX: { equationNumbers: { autoNumber: \"AMS\" } }\n",
-       "});\n"
-      ],
-      "text/plain": [
-       "<IPython.core.display.Javascript object>"
-      ]
-     },
-     "metadata": {},
-     "output_type": "display_data"
-    }
-   ],
+   "outputs": [],
    "source": [
-    "%%javascript\n",
-    "MathJax.Hub.Config({\n",
-    "    TeX: { equationNumbers: { autoNumber: \"AMS\" } }\n",
-    "});"
+    "# %%javascript\n",
+    "# MathJax.Hub.Config({\n",
+    "#     TeX: { equationNumbers: { autoNumber: \"AMS\" } }\n",
+    "# });"
    ]
   },
   {
@@ -54,6 +39,8 @@
    "source": [
     "## **1D monoatomic chain**\n",
     "$$\\require{cancel}$$\n",
+    "$$\\require{MathJax}$$\n",
+    "\n",
     "Let's now consider the case of a 1D monoatomic chain in which only the first neighbours interactions are considered. Let $R_n=na$ be the position of atom $n$, $R_{n+1}=(n+1)a$ the position of atom $n+1$, etc., as shown in Fig. 1. The classical equation of motion of the $n$-th atom of mass $M$ in position $R_n+u_n(t)$ under the force $F_n$ is:\n",
     "\\begin{equation}\n",
     "    M\\ddot u_n = -C_1(u_{n-1}-u_{n})-C_1(u_{n+1}-u_n)=-C_1(2u_n-u_{n-1}-u_{n+1})\n",
@@ -66,7 +53,7 @@
     "    \\label{eq:u_1d}\n",
     "\\end{equation}\n",
     "where $A$ is the amplitude of the displacement, $k$ is the phonon wave vector and $\\omega$ its frequency.<br>\n",
-    "Plugging Eq.\\eqref{eq:u_1d} into Eq.\\eqref{eq:1d_eq} results in\n",
+    "Plugging Eq.\\ref{eq:u_1d} into Eq.\\eqref{eq:1d_eq} results in\n",
     "$$\n",
     "\\begin{align}\n",
     "    -M \\omega^2 \\cancel{e^{ikn}}\\cancel{e^{-i\\omega t}} & =-C_1(2\\cancel{e^{ikn}}\\cancel{e^{-i\\omega t}}-\\cancel{e^{ikn}}\\cancel{e^{-i\\omega t}}e^{-ika}-\\cancel{e^{ikn}}\\cancel{e^{-i\\omega t}}e^{ika})\\nonumber \\\\\n",
@@ -79,13 +66,13 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 37,
+   "execution_count": 4,
    "metadata": {},
    "outputs": [
     {
      "data": {
       "text/html": [
-       "<img src=\"images/theory_phonon_1d_schematic.png\" style=\"margin:auto; width:40%\"/>\n",
+       "<img src=\"images/theory_phonon_1d_schematic.png\" style=\"margin:auto; width:50%\"/>\n",
        "<p style=\"text-align: center\">\n",
        "    Figure 1: Schematic of the 1D monoatomic chain.\n",
        "</p>\n"
diff --git a/notebook/lattice-vibration/theory/theory_phonon_2d.ipynb b/notebook/lattice-vibration/theory/theory_phonon_2d.ipynb
index 00236b2..4da1a74 100644
--- a/notebook/lattice-vibration/theory/theory_phonon_2d.ipynb
+++ b/notebook/lattice-vibration/theory/theory_phonon_2d.ipynb
@@ -7,7 +7,7 @@
     "# **Background theory**: Introduction to phonons\n",
     "<i class=\"fa fa-book fa-2x\"></i><a href=\"../Phonon_2D.ipynb\" style=\"font-size: 20px\"> Go back to the interactive notebook</a>\n",
     "\n",
-    "**Source code:** https://github.com/osscar-org/quantum-mechanics/tree/develop/notebook/lattice-vibration/theory/theory_phonon_2d.ipynb\n",
+    "**Source code:** https://github.com/osscar-org/quantum-mechanics/tree/master/notebook/lattice-vibration/theory/theory_phonon_2d.ipynb\n",
     "\n",
     "<hr style=\"height:1px;border:none;color:#cccccc;background-color:#cccccc;\" />"
    ]
@@ -19,7 +19,11 @@
    "outputs": [
     {
      "data": {
-      "application/javascript": "MathJax.Hub.Config({\n    TeX: { equationNumbers: { autoNumber: \"AMS\" } }\n});\n",
+      "application/javascript": [
+       "MathJax.Hub.Config({\n",
+       "    TeX: { equationNumbers: { autoNumber: \"AMS\" } }\n",
+       "});\n"
+      ],
       "text/plain": [
        "<IPython.core.display.Javascript object>"
       ]
@@ -29,10 +33,10 @@
     }
    ],
    "source": [
-    "%%javascript\n",
-    "MathJax.Hub.Config({\n",
-    "    TeX: { equationNumbers: { autoNumber: \"AMS\" } }\n",
-    "});"
+    "# %%javascript\n",
+    "# MathJax.Hub.Config({\n",
+    "#     TeX: { equationNumbers: { autoNumber: \"AMS\" } }\n",
+    "# });"
    ]
   },
   {
@@ -154,7 +158,7 @@
   "celltoolbar": "Aucun(e)",
   "hide_input": false,
   "kernelspec": {
-   "display_name": "Python 3.8.10 ('base')",
+   "display_name": "Python 3 (ipykernel)",
    "language": "python",
    "name": "python3"
   },
@@ -168,7 +172,7 @@
    "name": "python",
    "nbconvert_exporter": "python",
    "pygments_lexer": "ipython3",
-   "version": "3.8.10"
+   "version": "3.10.12"
   },
   "vscode": {
    "interpreter": {
@@ -177,5 +181,5 @@
   }
  },
  "nbformat": 4,
- "nbformat_minor": 2
+ "nbformat_minor": 4
 }