Section6.ipynb

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   "source": [
    "# Section 6: An Intuitive Picture of Band Structure"
   ]
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   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "from ipywidgets import interact, FloatSlider\n",
    "from IPython.display import display"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "96e29b11-0722-4084-badd-fab3dd0aa37d",
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   "source": [
    "In this Section, we are going to explore the emergence of band structure using simple models that you have studied before. We will consider a series of potential barriers (equally spaced) to simulate the periodic potential that electrons experience inside a crystal. By varying the heights of these barriers, we can smoothly transition between two simple limits: (1) a single, wide square well and (2) a series of narrow, uncoupled square wells. Band structure emerges between these two extremes. \n",
    "\n",
    "**Learning Goals**\n",
    "After this Section, you should:\n",
    "\n",
    "- Be able to explain the qualitative origins of energy bands\n",
    "- Explain the origin of energy spacings *within* bands as compared to *between* bands\n",
    "- Describe the shape of electronic wavefunctions at the edge of each Brillouin zone\n",
    "- Explain the connection between bound state and scattering methods of characterizing the energy levels of the periodic potential"
   ]
  },
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   "source": [
    "## Qualitative Solution"
   ]
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    "Before we dive into numerical solutions, let's think about the following qualitative situation: we have a square well of width $L$. Within the well, we place a series of barriers that partition the square well into $N$ narrower wells with width $a$. Each barrier has height $\\beta$ and thickness $b$. "
   ]
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    "Let's start by considering the barriers to be infinitely thin (basically, delta functions). Now, as a class, let's work through the following questions:\n",
    "\n",
    "1. What are the energies and eigenstates of the wide well if the barriers are not present ($\\beta=0$)?\n",
    "2. When $\\beta \\rightarrow \\infty$, what should the wavefunctions look like?\n",
    "3. As we increase $\\beta$ to take on finite values, what will happen to the wavefunctions? How will they look? What will their ordering be like relative to the cases we just described?\n",
    "4. What analogies could we make between excitation of different bands and excitations of atoms in a solid?"
   ]
  },
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   "source": [
    "After going through these qualitative arguments, we can now look at what the numerics tell us."
   ]
  },
  {
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   "source": [
    "## Building the potential V(x)"
   ]
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    "First we'll write some functions that build our model potential. Our model includes the following parameters:\n",
    "\n",
    "- $L$: width of the enclosing square well\n",
    "- $a$: width of each narrow square well\n",
    "- $b$: thickness of each internal barrier\n",
    "- $N$: number of narrow square wells\n",
    "- $\\beta$: heigh of each barrier.\n",
    "\n"
   ]
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  {
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    "#| echo: false\n",
    "# This function will return another function that depends only on x.\n",
    "# That's a convenient way to get a function of x that can go into our DVR code.\n",
    "# fullwidth allows us to embed the entire potential in a wider \"framing\" square well\n",
    "def make_potential(N, a, b, beta):\n",
    "    L = N*a+(N-2)*b\n",
    "    if N > 0:\n",
    "        x0s = np.arange(1,N)*(a+b)-(b) - L/2 # locations of barrier centers\n",
    "        def fn(x):\n",
    "            # builds a barrier of height beta and width b centered at each x0 value:\n",
    "            barriers = beta*np.sum([np.heaviside(x-x0s[n]+b/2 , 0.5) - np.heaviside((x-x0s[n]-b/2), 0.5) for n in range(N-1)], axis=0)\n",
    "            return barriers + beta * ((x < -L/2-b/2) | (x>L/2+b/2))\n",
    "    else:\n",
    "        a = L\n",
    "        def fn(x):\n",
    "            return np.zeros(len(x)) + beta * ((x < -L/2) | (x>L/2))\n",
    "    \n",
    "    return fn\n",
    "    "
   ]
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",
      "text/plain": [
       "<Figure size 1800x1200 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "#| echo: false\n",
    "f_test = make_potential(9, 1.1e-9, 0.1e-9, 1.5)\n",
    "x = np.linspace(-8,8, 5000)*1e-9\n",
    "plt.plot(x,f_test(x).T)\n",
    "plt.xlabel(\"x\")\n",
    "plt.ylabel(\"V\");"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "997ee79d-c4ad-470e-a339-3701ebe949ba",
   "metadata": {},
   "source": [
    "## Making the DVR code"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "480bd235-3bba-4d06-85c0-7222f0c40884",
   "metadata": {},
   "source": [
    "Next, we set up the DVR code from Section 4 to build the Hamiltonian for our system. This code is the same as we have used previously."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 68,
   "id": "145e1ae3-0982-4d21-ba8e-b0aca8a44540",
   "metadata": {
    "tags": [
     "hide-input"
    ]
   },
   "outputs": [],
   "source": [
    "hbar = (6.63e-34)/(2*np.pi) # in J.s\n",
    "m = 9.1e-31 # in kg\n",
    "\n",
    "# Function to make the kinetic energy operator\n",
    "def make_T(x):\n",
    "    Delta_x = x[1]-x[0]\n",
    "    N = x.shape[0]\n",
    "    Tmat = np.zeros((N,N))\n",
    "    \n",
    "    # now loop over kinetic energy matrix and fill in matrix elements\n",
    "    for i in range(N):\n",
    "        for j in range(N):\n",
    "            if i==j:\n",
    "                Tmat[i,j] = (hbar**2/(2*m*Delta_x**2)) * (np.pi**2)/3\n",
    "            else:\n",
    "                Tmat[i,j] = (hbar**2/(2*m*Delta_x**2)) * (-1)**(i-j) * 2/(i-j)**2\n",
    "                \n",
    "    return Tmat\n",
    "  \n",
    "# Function to make the potential energy operator\n",
    "def make_V(x,Vfunc):\n",
    "    Vmat = np.diag(Vfunc(x))\n",
    "    return Vmat\n",
    "\n",
    "# Function to make the full Hamiltonian\n",
    "def make_H(x,Vfunc):\n",
    "    return make_T(x) + make_V(x,Vfunc)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "ba6c449a-f623-4597-a412-a78e3316b4b4",
   "metadata": {},
   "source": [
    "Let's test this on a potential consisting of 12 wells that are fairly deep. After building the potential, we construct the Hamiltonian, evaluate the eigenvectors/eigenvalues, and then plot."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "d3f165fa-061d-4ee4-93de-9999d9df7a9c",
   "metadata": {
    "tags": [
     "hide-input"
    ]
   },
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "N = 12 # number of wells\n",
    "a = 0.4e-9\n",
    "b = 0.05e-9 # wall thickness in nm\n",
    "beta = 20 / 6.24150907e18 # well height in J\n",
    "V_wells = make_potential(N, a, b, beta)\n",
    "xs = np.linspace(-5, 5, 1600)*1e-9\n",
    "plt.plot(xs*1e9, V_wells(xs))\n",
    "plt.xlabel(\"Position (nm)\")\n",
    "plt.ylabel(\"Energy (eV)\")\n",
    "\n",
    "Ham=make_H(xs,V_wells)\n",
    "\n",
    "vals, vecs = np.linalg.eigh(Ham)\n",
    "# make sure ground state is upward going\n",
    "vecs[:,0] = vecs[:,0] * np.sign(vecs[np.argmax(np.abs(vecs[:,0])),0])\n",
    "# number of bound states:\n",
    "nbound = np.sum([vals<beta])"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "9929039f-328b-4fe9-ac3f-5936245020e8",
   "metadata": {},
   "source": [
    "We can now plot the numerically computed eigenvalues. Let's overlay these values with the energy levels that would occur if there were no barriers inside the potential---the energy levels of the \"wide\" finite square well."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 39,
   "id": "9c6f4e33-3dc5-4e98-af38-4186e371b9ab",
   "metadata": {
    "tags": [
     "hide-input"
    ]
   },
   "outputs": [],
   "source": [
    "def analytical_Es(w):\n",
    "    return [i**2 * np.pi**2 * hbar**2/(2*m*w**2) for i in range(1,nbound+1)]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 40,
   "id": "75e88aa3-7886-40c6-b6ef-89bd55f75e02",
   "metadata": {
    "tags": [
     "hide-input"
    ]
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x7fb5d3d27790>]"
      ]
     },
     "execution_count": 40,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(vals[:nbound],'.')\n",
    "plt.plot(analytical_Es(N*a+(N-2)*b))"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "9d866de3-c1a8-4fb5-b090-f3ff5d8b8232",
   "metadata": {},
   "source": [
    "Notice that the periodic potential leads to a structure highly reminiscient of band structure: the energy levels roughly follow the parabolic shape expected from the wide square well (or, from a different perspective, for the free particle), but the levels are broken up into bands with the characteristic shape that we see in class. And there are band gaps between these bands."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "ebdef0f9-d82a-440c-b9b7-9045e1bae47c",
   "metadata": {},
   "source": [
    "**Question: What will the plot look like if we increase the well separation to the point that the wells are essentially fully uncoupled? Will there be energy degeneracies? How many levels will share the same energy? What happens as the number of wells is increased--which energy gaps \"close\" and which remain?**\n",
    "\n",
    "To answer these questions, perform a \"numerical experiment\" and compare your results to the appropriate square well. How do the numbers compare?\n",
    "\n",
    "**Question: What happens if the well separation is decreased to essentially zero? How do these energies compare to the appropriate finite square well? What about the comparison to free particle energies?**"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "075b8fc3-8e2e-41ec-9763-30139c0e7606",
   "metadata": {},
   "source": [
    "Let's look at the wavefunctions to understand this even better. It will be useful to plot the actual wavefunctions and have some interactivity. The code below makes a plot with a slider that allows you to look at all of the bound eigenstates for a given potential. Once you set the number of wells, their width, and their barriers, you can scan through the eigenstates and look at the behavior."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 53,
   "id": "deb935d6-44f7-498b-bd8e-00c9f05d46df",
   "metadata": {
    "tags": [
     "hide-input"
    ]
   },
   "outputs": [],
   "source": [
    "def interact_wavefunction():        \n",
    "    ## Plot parameters\n",
    "    xmin, xmax, nx = min(xs)*1e9, max(xs)*1e9, 50\n",
    "    ymin, ymax = -1.2, 1.2\n",
    "    pmin, pmax, pstep, pinit = 0, nbound-1, 1, 0\n",
    "    \n",
    "    ## Set up the plot data\n",
    "    fig, (ax1,ax2)   = plt.subplots(1,2,figsize=(16,6))\n",
    "    line2, = ax1.plot(xs*1e9,2*V_wells(xs)/np.max(V_wells(xs))-1, color=\"grey\")\n",
    "    line, = ax1.plot([], [], linewidth=2, color=\"red\") # Initialize curve to empty data.\n",
    "    \n",
    "    well_levels, = ax2.plot([],[])\n",
    "    well_itself, = ax2.plot([],[], color=\"black\")\n",
    "\n",
    "    ## Set up the figure axes, etc.\n",
    "    ax1.set_xlim([xmin, xmax])\n",
    "    ax1.set_ylim([ymin, ymax])\n",
    "    ax2.set_xlim([xmin,xmax])\n",
    "    ax2.set_ylim([-beta/8*6.24150907e18,1.2*beta*6.24150907e18])\n",
    "    ax1.set_xlabel('Position (nm)', fontsize=18)\n",
    "    ax1.set_ylabel('Re{$\\psi$}', fontsize=18)\n",
    "    ax2.set_xlabel('Position (nm)', fontsize=18)\n",
    "    ax2.set_ylabel('Energy (eV)', fontsize=18)\n",
    "    ax1.tick_params(axis='both', which='major', labelsize=16)\n",
    "    ax2.tick_params(axis='both', which='major', labelsize=16)\n",
    "    plt.close()      # Don't show the figure yet.\n",
    "\n",
    "    ## Callback function\n",
    "    def plot_wavefunction(Eigenstate):\n",
    "        y = vecs[:,int(Eigenstate)]/np.max(np.abs(vecs[:,int(Eigenstate)]))\n",
    "        line.set_data(xs*1e9, y)\n",
    "        line2.set_data(xs*1e9, 2*V_wells(xs)/np.max(V_wells(xs))-1)\n",
    "        well_itself.set_data(xs*1e9, V_wells(xs)*6.24150907e18)\n",
    "        [ax2.axhline(y=vals[i]*6.24150907e18,color=\"grey\") for i in range(nbound)]\n",
    "        ax2.axhline(y=vals[int(Eigenstate)]*6.24150907e18, color=\"cyan\")\n",
    "        ax2.set_title(f\"E={np.round(vals[int(Eigenstate)]*6.24150907e18,3)} eV\", fontsize=16)\n",
    "        display(fig)\n",
    "\n",
    "    ## Generate the user interface.\n",
    "    interact(plot_wavefunction, \n",
    "             Eigenstate=FloatSlider(min=pmin, max=pmax, step=pstep, value=pinit))\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "8524bafc-ad4a-4e25-9215-becec6da2893",
   "metadata": {},
   "source": [
    "For example, we can start with 12 wells that are each 0.8 nm wide, 4 eV high, and have a 0.05 nm barrier between them. For this set of parameters, use the interactive plotting to gain some insights about the potential."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 54,
   "id": "cfd5f372-d440-4ced-baac-c7b39bdfd31d",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "427dec93a48d4e5eba5c9208ec62444f",
       "version_major": 2,
       "version_minor": 0
      },
      "text/plain": [
       "interactive(children=(FloatSlider(value=0.0, description='Eigenstate', max=32.0, step=1.0), Output()), _dom_cl…"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "N = 12 # number of wells\n",
    "a = 0.8e-9\n",
    "b = 0.05e-9 # wall thickness in nm\n",
    "beta = 4 / 6.24150907e18 # well height in J\n",
    "V_wells = make_potential(N, a, b, beta)\n",
    "xs = np.linspace(-8, 8, 900)*1e-9\n",
    "\n",
    "Ham=make_H(xs,V_wells)\n",
    "\n",
    "vals, vecs = np.linalg.eigh(Ham)\n",
    "# make sure ground state is upward going\n",
    "vecs[:,0] = vecs[:,0] * np.sign(vecs[np.argmax(np.abs(vecs[:,0])),0])\n",
    "# number of bound states:\n",
    "nbound = np.sum([vals<beta])\n",
    "\n",
    "\n",
    "interact_wavefunction();"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "9aed6f63-df8a-475b-9188-bd3ac3999206",
   "metadata": {},
   "source": [
    "**Question: Using the interactive graphs above, how does the behavior of each wavefunction within a single band conform to our expectations from Bloch's theorem? How do the wavefunctions differ from band to band? What do you expect to happen as $N \\rightarrow \\infty$?**"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "c180eaeb-2d63-4100-9dfe-f112edd393cb",
   "metadata": {},
   "source": [
    "## Transfer matrix approach"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "cb9a23ee-8e1b-4a17-a961-2eb320eabe82",
   "metadata": {},
   "source": [
    "There's a totally different way to look at band structure: by studying the scattering properties of the potential. This is a complementary method to learn about a potentials bound states. Scattering studies are widely used in many fields of physics/chemistry, from studying the solid state to studying atoms and molecules. Let's see what we can learn about electronic band structure from this point of view using the transfer matrix program that you wrote on HW2. "
   ]
  },
  {
   "cell_type": "markdown",
   "id": "9610bec7-856f-472c-b2b9-e1e6eb52e677",
   "metadata": {},
   "source": [
    "First of all, let's go over the idea of the transfer matrix approach.\n",
    "\n",
    "**Set up approach, talk about different role of propagation vs. transmission matrices.**\n",
    "\n",
    "The code to implement each of these matrices is copied below."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 55,
   "id": "50af1766-d06e-42b5-a32a-2d208c9a9b77",
   "metadata": {
    "tags": []
   },
   "outputs": [],
   "source": [
    "def DMat(k1, k2):\n",
    "    res = np.zeros((2,2),dtype=np.complex_)\n",
    "    res[0,0] = (1 + k2/k1)/2\n",
    "    res[0,1] = (1 - k2/k1)/2\n",
    "    res[1,0] = res[0,1]\n",
    "    res[1,1] = res[0,0]\n",
    "    return res\n",
    "\n",
    "def PMat(k, L):\n",
    "    res = np.zeros((2,2),dtype=np.complex_)\n",
    "    res[0,0] = np.exp(-1j * k * L)\n",
    "    res[1,1] = np.exp(1j * k * L)\n",
    "    return res"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "1c5a2bde-fd2e-4f10-8f11-c1226682ae0b",
   "metadata": {},
   "source": [
    "**Question: What do the peaks here represent? What is the physics going on when N=2? N=3? Large N?**"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 248,
   "id": "b9a0d549-b8f7-4076-b78b-bae82a9e284b",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "a = 0.8e-9\n",
    "b = 0.1e-9\n",
    "\n",
    "Es = np.arange(0.01, 12.0, 0.001) / 6.24150907e18\n",
    "width_barrier = b\n",
    "width_gap = a\n",
    "Vb=10/ 6.24150907e18\n",
    "\n",
    "Nwells=30\n",
    "\n",
    "\n",
    "Ttrans = np.zeros(Es.size)\n",
    "i = 0\n",
    "for E in Es:\n",
    "    klow = np.emath.sqrt(2 * m * E/hbar**2)\n",
    "    khigh = np.emath.sqrt(2 * m * (E - Vb)/hbar**2)\n",
    "    res_mat = DMat(klow, khigh) @ PMat(khigh, width_barrier) @ DMat(khigh, klow) @ PMat(klow, width_gap)\n",
    "    U, V = np.linalg.eig(res_mat)\n",
    "    diag_res_mat = np.diag([U[0],U[1]])\n",
    "    res_mat = np.linalg.matrix_power(diag_res_mat,Nwells)\n",
    "    res_mat = V @ res_mat @ np.linalg.inv(V)\n",
    "    Ttrans[i] = 1 - np.abs(res_mat[1, 0])**2 / np.abs(res_mat[0,0])**2\n",
    "    i = i + 1\n",
    "\n",
    "plt.plot(Es * 6.24150907e18, Ttrans)\n",
    "plt.xlabel(\"Energy (eV)\",fontsize=16)\n",
    "plt.ylabel(\"Transmission\",fontsize=16)\n",
    "plt.tick_params(axis='both', which='major', labelsize=16)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "fec5ebdc-fc6d-4758-b3a1-32986e29bd8e",
   "metadata": {},
   "source": [
    "Let's compare the transmission peaks to the bound state energy of our finite square well."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 249,
   "id": "a8991a8a-50d3-4011-a6dc-1ddf8f820f4e",
   "metadata": {},
   "outputs": [],
   "source": [
    "V_wells = make_potential(Nwells, a, b, Vb)\n",
    "xs = np.linspace(-15, 15, 1500)*1e-9\n",
    "\n",
    "Ham=make_H(xs,V_wells)\n",
    "\n",
    "vals, vecs = np.linalg.eigh(Ham)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "30accbf9-def3-4662-a1fe-c02321ee4bed",
   "metadata": {},
   "source": [
    "Now let's compare the transmission fraction to the band energies. \n",
    "\n",
    "**Question: How can we easily determine the limits of each energy band? (How does it compare to the number of wells being simulated?**"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 261,
   "id": "3e66f000-686a-4e5e-85c2-c39e8be9c09e",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(0.0, 10.0)"
      ]
     },
     "execution_count": 261,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "band_limits = [0]\n",
    "for n in range(5):\n",
    "    band_limits.append(n*Nwells-1)\n",
    "    band_limits.append(n*Nwells)\n",
    "\n",
    "plt.plot(Es * 6.24150907e18, Ttrans, color=\"limegreen\")\n",
    "[plt.axvline(vals[i]*6.24150907e18, color=\"black\") for i in band_limits]\n",
    "plt.xlabel(\"Energy (eV)\",fontsize=16)\n",
    "plt.ylabel(\"Transmission\",fontsize=16)\n",
    "plt.tick_params(axis='both', which='major', labelsize=16)\n",
    "plt.xlim(0,10)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "0d6e1d41-935d-45c1-b304-117c2d3076e2",
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3.9.7 ('base')",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.9.7"
  },
  "vscode": {
   "interpreter": {
    "hash": "40d3a090f54c6569ab1632332b64b2c03c39dcf918b08424e98f38b5ae0af88f"
   }
  }
 },
 "nbformat": 4,
 "nbformat_minor": 5
}