Final: Remove weird edge case from atomic_basis

I realized that the case of matching x[i] to mu[i] does not make any
sense.

Final/Final - Tight-binding propagation method.ipynb

@@ -232,7 +232,7 @@
     }
    ],
    "source": [
-    "def atomic_basis(x, mu, sigma, outer=False):\n",
+    "def atomic_basis(x, mu, sigma):\n",
     "    \"\"\"\n",
     "    Calculates the atomic basis functions for the 1D chain of atoms.\n",
     "    \n",
@@ -240,20 +240,14 @@
     "        x:     array of positions to calculate the wavefunction at\n",
     "        mu:    atomic position(s) to center Gaussian wavefunction at\n",
     "        sigma: broadening constant for Gaussian function(s)\n",
-    "        outer: if mu is an array: whether to calculate the atomic basis\n",
-    "               on a len(x) by len(mu) grid instead of the pairs x[i]\n",
-    "               and mu[i]\n",
     "\n",
     "    Returns:\n",
     "        An array of values for the wavefunction over the positions\n",
-    "        as given by x with shape len(x) by len(mu) if outer is False\n",
+    "        as given by x with shape len(x) by len(mu)\n",
     "    \"\"\"\n",
     "    \n",
-    "    if outer:\n",
     "    return np.pi**(-1/4)*sigma**(-1/2)*np.exp(-1/2*(np.subtract.outer(x, mu)/sigma)**2)\n",
     "\n",
-    "    return np.pi**(-1/4)*sigma**(-1/2)*np.exp(-1/2*((x - mu)/sigma)**2)\n",
-    "\n",
     "n = 10\n",
     "sigma = .25\n",
     "x = np.linspace(-2, 12, 1000)\n",
@@ -270,28 +264,6 @@
     "plt.show()"
    ]
   },
-  {
-   "cell_type": "code",
-   "execution_count": 15,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "(10000, 2)"
-      ]
-     },
-     "execution_count": 15,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "x = np.linspace(-1, 1, 10000)\n",
-    "mu = np.array([1,2])\n",
-    "atomic_basis(x, mu, .25, True).shape"
-   ]
-  },
   {
    "cell_type": "markdown",
    "metadata": {
@@ -1109,7 +1081,7 @@
     "    \n",
     "    # Luckily, the function is built in such a way it can also\n",
     "    # handle an array input as its first argument.\n",
-    "    delta = atomic_basis(w, Ei, sigma, True)\n",
+    "    delta = atomic_basis(w, Ei, sigma)\n",
     "    \n",
     "    rho = np.sum(delta, axis=1)\n",
     "    \n",