Final: Fix task 4.3 except for some TODOs and comments

Final/Final - Tight-binding propagation method.ipynb

@@ -1339,6 +1339,7 @@
     "    # And that indeed t[0] = 0*tau = 0.\n",
     "    assert np.allclose(t[0], 0)\n",
     "    \n",
+    "    # TODO: What should the dtype be, should it be complex?\n",
     "    c = np.zeros(t.shape + c0.shape, dtype=c0.dtype)\n",
     "    c[0] = c0\n",
     "    \n",
@@ -1440,16 +1441,7 @@
      "task": false
     }
    },
-   "outputs": [
-    {
-     "name": "stderr",
-     "output_type": "stream",
-     "text": [
-      "/tmp/ipykernel_2000248/327551893.py:14: ComplexWarning: Casting complex values to real discards the imaginary part\n",
-      "  c[j] = U@c[j - 1]\n"
-     ]
-    }
-   ],
+   "outputs": [],
    "source": [
     "n = 100\n",
     "# TODO: Should one be able to pass a through everything?\n",
@@ -1460,15 +1452,18 @@
     "\n",
     "H = TBHamiltonian(n, sigma)\n",
     "U = getU_exact(tau, H)\n",
-    "#c0 = np.zeros(n, dtype=np.complex128)\n",
-    "c0 = np.zeros(n)\n",
+    "# TODO: Is c0 complex?\n",
+    "c0 = np.zeros(n, dtype=np.complex128)\n",
+    "#c0 = np.zeros(n)\n",
     "c0[n//2] = 1\n",
     "\n",
     "c = timePropagate(U, c0, t)\n",
     "xi = atomic_positions(n, a)\n",
-    "psi = c@atomic_basis(x, xi, sigma).T\n",
-    "\n",
-    "x = np.linspace(-1, 11, 150)"
+    "x = np.linspace(-1, 101, 150)\n",
+    "# TODO: Does real-space wavefunction mean that it should be real or\n",
+    "#       that we take the real part?\n",
+    "psi = np.real(c@atomic_basis(x, xi, sigma).T)\n",
+    "\n"
    ]
   },
   {
@@ -1477,6 +1472,8 @@
    "metadata": {},
    "outputs": [],
    "source": [
+    "psi\n",
+    "\n",
     "# This cell can be deleted!\n",
     "x = np.linspace(-1, 11, 150)\n",
     "xi = atomic_positions(n, a)\n",
@@ -1488,8 +1485,8 @@
     "#print(psi)\n",
     "psi.shape\n",
     "#psi[t][x]\n",
-    "plt.plot(x, psi[30])\n",
-    "print(psi[2].shape, x.shape)"
+    "plt.plot(x, psi[20])\n",
+    "print(psi[100].shape, x.shape)"
    ]
   },
   {
@@ -1521,8 +1518,8 @@
     "# create a figure for the animation\n",
     "fig = plt.figure()\n",
     "plt.grid(True)\n",
-    "plt.xlim(-1, 11)     # fix x limits\n",
-    "plt.ylim(-1e-6, 1e-6)     # fix y limits\n",
+    "plt.xlim(-1, 101)     # fix x limits\n",
+    "plt.ylim(-.5, .6)     # fix y limits\n",
     "plt.xlabel('$x$')\n",
     "plt.ylabel('$\\\\psi(t, x)$')\n",
     "\n",