Final: Comment on integration limits in 3.1

Final/Final - Tight-binding propagation method.ipynb

@@ -631,9 +631,13 @@
     "    sigma = .25\n",
     "    positions = atomic_positions(n)\n",
     "    \n",
-    "    infty = 1e3\n",
-    "    epsilon = 1e-3\n",
-    "    x = np.arange(-infty, infty, epsilon)\n",
+    "    # This 'infinity' is large enough, as the Gaussians decay quite quickly\n",
+    "    # away from the atomic positions, which we already saw in the overlap\n",
+    "    # above.\n",
+    "    # TODO: Remember https://www.wolframalpha.com/input?i=integrate+1%2F%28.25*sqrt%282pi%29%29*exp%28-.5*%28x%2F.25%29%5E2%29+for+x%3D-1..1.\n",
+    "    infty = 1e2\n",
+    "    h = 1e-6\n",
+    "    x = np.arange(-infty, infty, h)\n",
     "    \n",
     "    def V(x):\n",
     "         ret = np.zeros(x.shape)\n",
@@ -683,12 +687,12 @@
      "name": "stdout",
      "output_type": "stream",
      "text": [
-      "-0.13881260449985544 -0.13881260449985544\n"
+      "-3.08808170797426e-06 -0.13849169656144708\n"
      ]
     }
    ],
    "source": [
-    "print(hopping(1, 0, 10), hopping(0, 1, 10))\n",
+    "print(hopping(0, 2, 10), hopping(0, 1, 10))\n",
     "\n",
     "# YOUR CODE HERE\n",
     "#raise NotImplementedError()"