diff --git a/Final/Final - Tight-binding propagation method.ipynb b/Final/Final - Tight-binding propagation method.ipynb
index 81932a0..7432e96 100644
--- a/Final/Final - Tight-binding propagation method.ipynb	
+++ b/Final/Final - Tight-binding propagation method.ipynb	
@@ -86,7 +86,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 1,
+   "execution_count": 3,
    "metadata": {
     "deletable": false,
     "nbgrader": {
@@ -135,7 +135,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 2,
+   "execution_count": 4,
    "metadata": {
     "deletable": false,
     "nbgrader": {
@@ -202,7 +202,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 3,
+   "execution_count": 5,
    "metadata": {
     "deletable": false,
     "nbgrader": {
@@ -289,7 +289,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 4,
+   "execution_count": 6,
    "metadata": {
     "deletable": false,
     "nbgrader": {
@@ -342,7 +342,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 5,
+   "execution_count": 7,
    "metadata": {
     "deletable": false,
     "nbgrader": {
@@ -398,7 +398,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 6,
+   "execution_count": 8,
    "metadata": {
     "deletable": false,
     "nbgrader": {
@@ -606,7 +606,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": null,
+   "execution_count": 114,
    "metadata": {
     "deletable": false,
     "nbgrader": {
@@ -628,8 +628,26 @@
     "    \n",
     "    \"\"\"\n",
     "    \n",
-    "    x = np.linspace(-1e12, 1e12, 1e12)\n",
-    "    V = lambda x: -1 \n",
+    "    sigma = .25\n",
+    "    positions = atomic_positions(n)\n",
+    "    \n",
+    "    infty = 1e3\n",
+    "    epsilon = 1e-5\n",
+    "    x = np.arange(-infty, infty, epsilon)\n",
+    "    \n",
+    "    # V is calculated by creating a matrix len(x) by len(positions) over which\n",
+    "    # we sum each row to create a matching value V(x) for each element of x.\n",
+    "    #V = lambda x: np.sum(-1/(np.abs(x - positions)) + 0.001, axis=1)\n",
+    "    #V = lambda x: np.sum( -1/( x - np.tile(positions, (len(x), 1)).T) + 0.001 ), axis=0 )\n",
+    "    def V(x):\n",
+    "         value = np.zeros(x.shape)\n",
+    "         for x_i in positions:\n",
+    "             value += -1./(np.abs(x - x_i) + 0.001)\n",
+    "         return value\n",
+    "    #V = lambda x: np.sum( -1/( np.abs(np.tile(x, (len(positions), 1)) - np.tile(positions, (len(x), 1)).T) + 0.001 ), axis=0 )\n",
+    "    #V = lambda x: np.sum( -1/( np.abs(x - np.tile(positions, (len(x), 1)).T) + 0.001 ), axis=0 )\n",
+    "    # OMG IT EXISTS\n",
+    "    #V = lambda x: np.sum( -1/( np.abs(np.subtract.outer(x, positions)) + 0.001 ), axis=1 )\n",
     "    integrand = lambda x: atomic_basis(x, positions[i], sigma)*V(x)*atomic_basis(x, positions[j], sigma)\n",
     "    return integrate(integrand, x)\n",
     "\n",
@@ -645,7 +663,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": null,
+   "execution_count": 115,
    "metadata": {
     "deletable": false,
     "nbgrader": {
@@ -660,12 +678,21 @@
      "task": false
     }
    },
-   "outputs": [],
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "21.9 s ± 35.9 ms per loop (mean ± std. dev. of 7 runs, 1 loop each)\n"
+     ]
+    }
+   ],
    "source": [
-    "# Verify that long-range hoppings are negligible here ...\n",
+    "#print(hopping(1, 0, 10), hopping(0, 1, 10))\n",
+    "%timeit hopping(1, 0, 10)\n",
     "\n",
     "# YOUR CODE HERE\n",
-    "raise NotImplementedError()"
+    "#raise NotImplementedError()"
    ]
   },
   {