{
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  {
   "cell_type": "markdown",
   "id": "reliable-developer",
   "metadata": {},
   "source": [
    "# Plotting Wavefunctions of the Quantum Harmonic Oscillator (LC Circuit) "
   ]
  },
  {
   "cell_type": "markdown",
   "id": "incident-serial",
   "metadata": {},
   "source": [
    "Let's start by importing qiskit metal as well as some helpful libraries for math and plotting:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "scenic-motor",
   "metadata": {},
   "outputs": [],
   "source": [
    "import qiskit_metal as metal\n",
    "import matplotlib.pyplot as plt\n",
    "import numpy as np\n",
    "import math "
   ]
  },
  {
   "cell_type": "markdown",
   "id": "unnecessary-harvard",
   "metadata": {},
   "source": [
    "Next, let's import the function \"wavefunction\" from the file \"HO_wavefunctions.py\" located in the analyses / hamiltonian folder. This function takes four arguments: the inductance (L), the capacitance (C), the energy level of the harmonic oscillator (n) and the values of charge (x=Q) for which the wavefunctions are calculated. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "wicked-commissioner",
   "metadata": {},
   "outputs": [],
   "source": [
    "from qiskit_metal.analyses.hamiltonian.HO_wavefunctions import wavefunction"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "fresh-spare",
   "metadata": {},
   "source": [
    "We'll define the charge to be in the range (-5,5) with 100 points in between. For simplicity, we'll set L=C=1.0 in the examples below. We can plot the first five energy levels (N=0 through N=4) of the quantum oscillator by executing the code below: "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "obvious-arrival",
   "metadata": {},
   "outputs": [],
   "source": [
    "# Let's define the range of x-axis values (representating charge) to be from (-5,5) \n",
    "x = np.linspace(-5,5,100)\n",
    " \n",
    "# Let's plot the first five energy levels (N=0 through N=4) of the harmonic oscillator\n",
    "# We'll just take L=C=1.0 for simplicity \n",
    "plt.plot(x, wavefunction(1.0, 1.0, 0.0, x), 'k') # N=0; ground state (black)\n",
    "plt.plot(x, wavefunction(1.0, 1.0, 1.0, x), 'b') # N=1; first excited state (blue)\n",
    "plt.plot(x, wavefunction(1.0, 1.0, 2.0, x), 'r') # N=2; second excited state (red)\n",
    "plt.plot(x, wavefunction(1.0, 1.0, 3.0, x), 'g') # N=3; third excited state (green)\n",
    "plt.plot(x, wavefunction(1.0, 1.0, 4.0, x), 'y') # N=4; fourth excited state (yellow) \n",
    "plt.xlabel(\"Charge [Q]\")\n",
    "plt.ylabel(\"Wavefunction [Psi]\")\n",
    "\n",
    "# show the plot\n",
    "plt.show()"
   ]
  }
 ],
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