{
 "cells": [
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   "source": [
    "# Nuclear Basis Set\n",
    "## Overview\n",
    "In this notebook, we will introduce the basics of nuclear basis sets. We will start from harmonic oscillator eigenbasis and then introduce discrete value represetation (DVR).\n",
    "In the end we will present the variational calculation of the ground state energy and wavefunction of a displaced harmonic oscillator.\n",
    "The purpose of this notebook is to elaborate the basic funtionality of the nuclear basis set. Tensor network algorithms are not covered in this notebook.\n",
    "\n",
    "## The basis sets\n",
    "The harmonic eigenfunctions are\n",
    "\n",
    "$$\n",
    "\\psi_\\nu(\\xi) = N_\\nu H_\\nu(\\xi) e^{-\\xi^2/2}\n",
    "$$\n",
    "\n",
    "where $\\nu$ is the energy level or the quantum number，$H_\\nu(\\xi)$ is the Hermite polnomial, $\\xi=\\frac{x}{\\alpha}$ is the unitless coordiate，$\\alpha=\\sqrt{\\frac{\\hbar}{m\\omega}}$，$N_\\nu = \\sqrt{\\frac{1}{\\alpha 2^\\nu \\nu! \\pi^{\\frac{1}{2}}}}$ is the normalization constant.\n",
    "We will use $\\hbar=m=\\omega=1$ throughout this notebook."
   ]
  },
  {
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     "text": [
      "2026-10-14 01:46:09,932[INFO] Use numpy as backend\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "2026-10-14 01:46:09,935[INFO] numpy random seed is 9012\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "2026-10-14 01:46:09,936[INFO] backend random seed is 2019\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "2026-10-14 01:46:09,936[INFO] random seed is 1092\n"
     ]
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    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "2026-10-14 01:46:09,944[INFO] Git Commit Hash: 3507afde83fd6f408c1c2198aad4dfe455d88312\n"
     ]
    }
   ],
   "source": [
    "from math import factorial\n",
    "\n",
    "from renormalizer import Op, Model, Mpo, BasisSHO, BasisSimpleElectron\n",
    "from renormalizer.utils.log import set_stream_level, INFO\n",
    "set_stream_level(INFO)\n",
    "\n",
    "import numpy as np\n",
    "from scipy.special import eval_hermite as hermite\n",
    "from matplotlib import pyplot as plt\n",
    "plt.style.use(\"mm.mplstyle\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "43e06282-3791-4bd6-938f-90aa18a04352",
   "metadata": {
    "execution": {
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   "outputs": [],
   "source": [
    "omega = 1"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "c41a8dc5-28a3-403c-bcfd-39087875764e",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-10-14T01:46:12.812034Z",
     "iopub.status.busy": "2026-10-14T01:46:12.811838Z",
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   "outputs": [],
   "source": [
    "# calculate and store the lowest 16 wavefuntions for the following visualization\n",
    "limit = 6\n",
    "xi = np.linspace(-limit, limit, 10000)\n",
    "psi_list = []\n",
    "for nu in range(16):\n",
    "    n = np.sqrt(1/(2**nu*factorial(nu)*np.pi**0.5))\n",
    "    psi = n * hermite(nu, xi) * np.exp(-xi ** 2/ 2)\n",
    "    psi_list.append(psi)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "c9183f3b-79ce-4c2d-a283-5d35360b2728",
   "metadata": {},
   "source": [
    "We first plot the wavefuntion of the lowest 4 states. Then we plot the DVR from the lowest 7 states. DVR states are eigenstates of the position operator. 4 out of 7 DVR states are plotted for clarity.\n",
    "The DVR transformation matrix is calculated by the ``BasisSHO`` class."
   ]
  },
  {
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     "shell.execute_reply": "2026-10-14T01:46:17.460433Z"
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   "outputs": [
    {
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",
      "text/plain": [
       "<Figure size 800x300 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "n_basis = 7\n",
    "basis = BasisSHO(0, omega=omega, nbas=n_basis, dvr=True)\n",
    "\n",
    "fig, axs = plt.subplots(1, 2, figsize=(8, 3), sharey=True)\n",
    "\n",
    "plt.sca(axs[0])\n",
    "for i in range(4):\n",
    "    plt.plot(xi, psi_list[i], label=r\"$\\varphi_\" + str(i) + \"$\")\n",
    "plt.title(\"(a) Harmonic Oscillator Eigenbasis\")\n",
    "plt.xlabel(\"$x$\")\n",
    "plt.ylabel(\"Amplitude\")\n",
    "plt.legend()\n",
    "\n",
    "plt.sca(axs[1])\n",
    "for i in range(n_basis):\n",
    "    phi = basis.dvr_v[:, i] @ np.array(psi_list)[:n_basis]\n",
    "    # adjust the phase for clarity\n",
    "    if phi[np.argmax(np.abs(phi))] < 0:\n",
    "        phi = -phi\n",
    "    if i % 2 == 0:\n",
    "        plt.plot(xi, phi, label=r\"$\\phi_\" + str(i) + \"$\")\n",
    "        \n",
    "plt.title(\"(b) Harmonic Oscillator DVR\")\n",
    "plt.xlabel(\"$x$\")\n",
    "plt.legend()\n",
    "\n",
    "plt.tight_layout()\n",
    "plt.savefig(\"sho.pdf\")\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "b7dca69f-15fc-4b6d-82a1-c75e3ad79f5e",
   "metadata": {},
   "source": [
    "## Variational calculation\n",
    "We variationally calculate of the ground state energy and wavefunction of a displaced harmonic oscillator using the ``BasisSHO`` basis set.\n",
    "The Hamiltonian is written as\n",
    "\n",
    "$$\n",
    "H = -\\frac{1}{2m}\\frac{d^2}{dx^2} + \\frac{1}{2} m\\omega^2 (x-x_{\\textrm{eq}})^2\n",
    "$$\n",
    "\n",
    "In second-quantization, it is written as\n",
    "\n",
    "$$\n",
    "H =\\omega b^\\dagger b + g\\omega(b^\\dagger + b) + E_{\\textrm{shift}}\n",
    "$$\n",
    "\n",
    "where $g=-\\sqrt{\\frac{m\\omega}{2}} x_{\\textrm{eq}}$ and $E_{\\textrm{shift}}=\\frac{1}{2}m\\omega^2x_{\\textrm{eq}}^2+\\frac{1}{2}\\omega$ are constants.\n",
    "\n",
    "We label the DOF of this nuclear coordiate as ``0``, and construct the Hamiltonian using the ``Op`` class.\n",
    "The Hamiltonian matrix is calculated by constructing an MPO with only 1 site.\n",
    "\n",
    "We perform the calculation at several different values of $x_{\\textrm{eq}}$ and the number of basis in the basis set."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "9dce33c0-e5d1-4232-b2fc-993d30528a2a",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-10-14T01:46:17.463299Z",
     "iopub.status.busy": "2026-10-14T01:46:17.463137Z",
     "iopub.status.idle": "2026-10-14T01:46:17.505757Z",
     "shell.execute_reply": "2026-10-14T01:46:17.504968Z"
    }
   },
   "outputs": [],
   "source": [
    "e_list = []\n",
    "wfn_list = []\n",
    "nbas_list = [4, 8, 16]\n",
    "x_eq_range = np.linspace(1, 3, 10)\n",
    "for n_basis in nbas_list:\n",
    "    e_list.append([])\n",
    "    for x_eq in x_eq_range:\n",
    "        g = -np.sqrt(omega/2) * x_eq\n",
    "    \n",
    "        ham = omega * Op(r\"b^\\dagger b\", 0) + g * omega * Op(\"b^\\dagger+b\", 0)\n",
    "        constant = omega / 2 + omega ** 2 * x_eq ** 2 / 2\n",
    "        \n",
    "        basis = [BasisSHO(0, nbas=n_basis, omega=omega)]\n",
    "        model = Model(basis, ham)\n",
    "        h = Mpo(model).todense()\n",
    "        evals, evecs = np.linalg.eigh(h)\n",
    "        e = evals[0]\n",
    "        e_list[-1].append(e + constant)\n",
    "        if x_eq == x_eq_range[-1]:\n",
    "            wfn_list.append(evecs[:, 0])"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "f9960063-f6cd-4e79-9101-e46ade60fdc2",
   "metadata": {},
   "source": [
    "When $x_{\\textrm{eq}}$ is small, say 1, we see that using 4 basis states are enough for accurate result.\n",
    "However, when $x_{\\textrm{eq}}$ increases to around 3, using 4 basis states has a large error.\n",
    "If we employ 16 basis states instead, the error is suppressed. \n",
    "We expect that even more states will be required if $x_{\\textrm{eq}}$ continues to increase."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "fab4d11e-80b7-4eac-b240-69c5a300a7d4",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-10-14T01:46:17.507655Z",
     "iopub.status.busy": "2026-10-14T01:46:17.507502Z",
     "iopub.status.idle": "2026-10-14T01:46:21.323023Z",
     "shell.execute_reply": "2026-10-14T01:46:21.322071Z"
    }
   },
   "outputs": [
    {
     "data": {
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",
      "text/plain": [
       "<Figure size 800x300 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, axs = plt.subplots(1, 2, figsize=(8, 3))\n",
    "plt.sca(axs[0])\n",
    "\n",
    "labels = [f\"$N={i}$\" for i in nbas_list]\n",
    "markers = [\"s\", \"o\", \"x\"]\n",
    "for i in range(3):\n",
    "    plt.plot(x_eq_range, e_list[i], label=labels[i], marker=markers[i])\n",
    "plt.plot(x_eq_range, np.ones(len(x_eq_range)) * 0.5, label=\"Exact\", linestyle=\":\")\n",
    "plt.xlabel(r\"$x_{\\textrm{eq}}$\")\n",
    "plt.ylabel(\"$E$\")\n",
    "plt.title(\"(a) Variational Energy\")\n",
    "plt.legend()\n",
    "\n",
    "plt.sca(axs[1])\n",
    "for i in range(3):\n",
    "    phi =  wfn_list[i] @ psi_list[:nbas_list[i]]\n",
    "    if phi[np.argmax(np.abs(phi))] < 0:\n",
    "        phi = -phi\n",
    "    plt.plot(xi, phi, label=labels[i])\n",
    "n = np.sqrt(1/(np.pi**0.5))\n",
    "plt.plot(xi, n * hermite(0, xi-3) * np.exp(-(xi-3) ** 2/ 2), linestyle=\":\", label=\"Exact\")\n",
    "plt.xlabel(\"$x$\")\n",
    "plt.ylabel(\"Amplitude\")\n",
    "plt.title(\"(b) Variational Wavefunction\")\n",
    "plt.legend()\n",
    "\n",
    "plt.tight_layout()\n",
    "plt.savefig(\"sho_variational.pdf\")\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "d792525f-6215-436e-a923-fbaa4ffa2c29",
   "metadata": {},
   "source": [
    "## Notes on the truncation level or number of basis states\n",
    "In tensor network calculations, the number of basis functions for each phonon mode is another parameter that must be checked for convergence manually. A common starting point is to set this number to 16.\n",
    "\n",
    "At zero temperature, the required number of basis functions is primarily determined by the coupling strength. \n",
    "\n",
    "If there are a lot of different modes in the model, setting the number of basis states to the same number can be inefficient. \n",
    "An empirical and usually safe estimate of the number of basis states, adaptive to the coupling strength, is given by\n",
    "$$\\rm{max}(16c^2/\\omega^3, 4)$$\n",
    "where $c$ is the coupling strength constant in coupling terms such as $cx\\sigma_z$. Note that $c^2/2\\omega^3$ is the Huang–Rhys factor.\n",
    "\n",
    "At finite temperature, temperature also influences the required basis size: higher temperatures generally require more basis functions.\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "226c18fb-b9a9-4136-9677-6b99eaef34ca",
   "metadata": {},
   "source": [
    "## Nuclear basis sets in Renormalizer\n",
    "### `BasisSHO`\n",
    "The most commonly used nuclear basis set is `BasisSHO`, which has been demonstrated above. The basis set is best used with second-quantization.\n",
    "If the nuclear DoF is a harmonic oscillilator, using `BasisSHO` usually shows fastest convergence of the number of bases, particularly for high frequency or low coupling-strength modes.\n",
    "In these cases, using 4 bases is sometimes sufficient to obtain very accurate result.\n",
    "Besides, the ground state can be easily specified as `[1, 0, 0, ..., 0]`.\n",
    "\n",
    "#### Basic Usage\n",
    "In the following we employ `nbas=4` for demonstration purposes. As mentioned above usually 16 bases are a good starting point for production calculation."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "7e742895-d3b8-4795-852d-6275c265ce88",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-10-14T01:46:21.324996Z",
     "iopub.status.busy": "2026-10-14T01:46:21.324799Z",
     "iopub.status.idle": "2026-10-14T01:46:21.329495Z",
     "shell.execute_reply": "2026-10-14T01:46:21.328693Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[0., 0., 0., 0.],\n",
       "       [0., 1., 0., 0.],\n",
       "       [0., 0., 2., 0.],\n",
       "       [0., 0., 0., 3.]])"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "omega = 2\n",
    "basis = BasisSHO(0, omega=omega, nbas=4)\n",
    "basis.op_mat(\"b^\\dagger b\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "id": "ebeb6474-d2dc-477d-bdee-96bac61de49d",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-10-14T01:46:21.331090Z",
     "iopub.status.busy": "2026-10-14T01:46:21.330928Z",
     "iopub.status.idle": "2026-10-14T01:46:21.335003Z",
     "shell.execute_reply": "2026-10-14T01:46:21.334145Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[0.        , 1.        , 0.        , 0.        ],\n",
       "       [1.        , 0.        , 1.41421356, 0.        ],\n",
       "       [0.        , 1.41421356, 0.        , 1.73205081],\n",
       "       [0.        , 0.        , 1.73205081, 0.        ]])"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "basis.op_mat(\"b^\\dagger+b\")"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "8f1b3aca-9ca9-4653-a866-46cc614d03b0",
   "metadata": {},
   "source": [
    "The operators supported by the basis set include `\"b^\\dagger b\"`, `\"b^\\dagger+b\"`, `\"b^\\dagger-b\"` and so on.\n",
    "\n",
    "The basis set also supports first-quantized operators, following\n",
    "$$\n",
    "x = \\frac{1}{\\sqrt{2\\omega}} (b^\\dagger + b)\n",
    "$$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "id": "5a6a7c15-f059-47ed-8fba-975582a17845",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-10-14T01:46:21.336816Z",
     "iopub.status.busy": "2026-10-14T01:46:21.336664Z",
     "iopub.status.idle": "2026-10-14T01:46:21.340554Z",
     "shell.execute_reply": "2026-10-14T01:46:21.339725Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[0.        , 0.5       , 0.        , 0.        ],\n",
       "       [0.5       , 0.        , 0.70710678, 0.        ],\n",
       "       [0.        , 0.70710678, 0.        , 0.8660254 ],\n",
       "       [0.        , 0.        , 0.8660254 , 0.        ]])"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "basis.op_mat(\"x\")"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "df5a59fe-1e2a-4f8c-bb6e-66c22f459a81",
   "metadata": {},
   "source": [
    "The mass is assumed to be 1, or scaled into $x$. \n",
    "\n",
    "The energy operator in terms of $x$ and $p$ is given by \n",
    "$$\n",
    "H = \\frac{1}{2} p^2 + \\frac{1}{2} \\omega^2 x^2\n",
    "$$\n",
    "or the following code"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "id": "eea8d09c-e3df-4e35-8ee5-a01567454e8c",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-10-14T01:46:21.342257Z",
     "iopub.status.busy": "2026-10-14T01:46:21.342105Z",
     "iopub.status.idle": "2026-10-14T01:46:21.346491Z",
     "shell.execute_reply": "2026-10-14T01:46:21.345688Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[1., 0., 0., 0.],\n",
       "       [0., 3., 0., 0.],\n",
       "       [0., 0., 5., 0.],\n",
       "       [0., 0., 0., 7.]])"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "basis.op_mat(\"p^2\")/2 + 1/2 * omega** 2 * basis.op_mat(\"x^2\")"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "f1b2f84e-9c9a-47df-bcf9-1f9c6819fd9d",
   "metadata": {},
   "source": [
    "#### DVR basis\n",
    "To use grid basis (DVR) based on `BasisSHO`, set `dvr=True`. The `x` matrix then becomes diagonal."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "id": "6b909bd3-1782-4e83-ad61-2d5d0820d860",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-10-14T01:46:21.348216Z",
     "iopub.status.busy": "2026-10-14T01:46:21.348065Z",
     "iopub.status.idle": "2026-10-14T01:46:21.352873Z",
     "shell.execute_reply": "2026-10-14T01:46:21.351850Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[-1.16720711,  0.        ,  0.        ,  0.        ],\n",
       "       [ 0.        , -0.37098189,  0.        ,  0.        ],\n",
       "       [ 0.        ,  0.        ,  0.37098189,  0.        ],\n",
       "       [ 0.        ,  0.        ,  0.        ,  1.16720711]])"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "basis = BasisSHO(0, omega=omega, nbas=4, dvr=True)\n",
    "basis.op_mat(\"x\")"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "c41ba158-b0d9-4d7c-b784-fd3b56611783",
   "metadata": {},
   "source": [
    "The grid points are accessible from `basis.dvr_x`"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "id": "6e79927f-030a-49c7-800e-89e3f864e246",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-10-14T01:46:21.354468Z",
     "iopub.status.busy": "2026-10-14T01:46:21.354317Z",
     "iopub.status.idle": "2026-10-14T01:46:21.358014Z",
     "shell.execute_reply": "2026-10-14T01:46:21.357192Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([-1.16720711, -0.37098189,  0.37098189,  1.16720711])"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "basis.dvr_x"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "403aa417-d02a-41f9-9f1c-740860cfae75",
   "metadata": {},
   "source": [
    "In DVR basis, the Hamiltonian matrix is not diagonal anymore."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "id": "c45927ba-4734-4b89-a2b3-3ff39bd56b68",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-10-14T01:46:21.359835Z",
     "iopub.status.busy": "2026-10-14T01:46:21.359667Z",
     "iopub.status.idle": "2026-10-14T01:46:21.364107Z",
     "shell.execute_reply": "2026-10-14T01:46:21.363212Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 4.31649658, -1.07735027, -0.07735027,  0.31649658],\n",
       "       [-1.07735027,  2.68350342, -1.31649658, -0.07735027],\n",
       "       [-0.07735027, -1.31649658,  2.68350342, -1.07735027],\n",
       "       [ 0.31649658, -0.07735027, -1.07735027,  4.31649658]])"
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "h_mat = basis.op_mat(\"p^2\")/2 + 1/2 * omega** 2 * basis.op_mat(\"x^2\")\n",
    "h_mat"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "2b0bd16b-9cff-4606-adc8-b2011ff3b86e",
   "metadata": {},
   "source": [
    "However, we can still reliably obtain the low-energy spectrum"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "id": "e3ec329c-38e7-4863-b5d9-06e4d22e5631",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-10-14T01:46:21.365707Z",
     "iopub.status.busy": "2026-10-14T01:46:21.365557Z",
     "iopub.status.idle": "2026-10-14T01:46:21.369379Z",
     "shell.execute_reply": "2026-10-14T01:46:21.368593Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([1., 3., 5., 5.])"
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.linalg.eigvalsh(h_mat)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "9bde42a7-8e7f-47ad-a09b-38a10a9601cf",
   "metadata": {},
   "source": [
    "With `dvr=True`, second-quantized operators such as `\"b^\\dagger + b\"` become ill-defined. Do not mix DVR with second-quantization."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "4a866762-3648-44cb-ab4c-1d783afc2a68",
   "metadata": {},
   "source": [
    "Note that when `dvr=True`, the ground state is not `[1, 0, 0, ..., 0]` anymore. You need to compute the wavefunction amplitudes on the grid points `basis.dvr_x`."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "b5e89e61-2445-45a1-93e1-b6eb90a4e549",
   "metadata": {},
   "source": [
    "#### Dimensionless coordinate and momentum\n",
    "\n",
    "By default, the coordinate $x$ and momentum $p$ in Renormalizer and `BasisSHO` are dimensional.\n",
    "\n",
    "Sometimes, it is desirable to use dimensionless $x$ and $p$ by scaling with $\\omega$\n",
    "$$\n",
    "x \\rightarrow \\sqrt{\\omega}x\n",
    "$$\n",
    "$$\n",
    "p \\rightarrow p/\\sqrt{\\omega}\n",
    "$$\n",
    "The Hamiltonian is then expressed as\n",
    "$$\n",
    "H = \\frac{\\omega}{2} (p^2 + x^2)\n",
    "$$\n",
    "which shows a closer connection to the second-quantized form.\n",
    "\n",
    "To scale $x$ and $p$ with $\\omega$, such that the Hamiltonian can be written as $\\frac{\\omega}{2}(p^2+x^2)$, set `scale_omega=True` when intializing the basis set."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "id": "2f169161-8084-48d0-a768-57d6e7797668",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-10-14T01:46:21.371322Z",
     "iopub.status.busy": "2026-10-14T01:46:21.371173Z",
     "iopub.status.idle": "2026-10-14T01:46:21.376494Z",
     "shell.execute_reply": "2026-10-14T01:46:21.375688Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([1., 3., 5., 5.])"
      ]
     },
     "execution_count": 15,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "basis = BasisSHO(0, omega=omega, nbas=4, dvr=True, scale_omega=True)\n",
    "# The harmonic oscillator Hamiltonian with the dimensionless x and p\n",
    "h_mat = 1/2 * omega * (basis.op_mat(\"p^2\") + basis.op_mat(\"x^2\"))\n",
    "np.linalg.eigvalsh(h_mat)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "ddecc430-fe7f-447c-a467-bb080256445a",
   "metadata": {},
   "source": [
    "The effect is the same as setting `omega=1` when creating the `BaisSHO` instance."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "id": "a4d97113-5c5a-4cb6-a4ed-c303b29d5e6d",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-10-14T01:46:21.378122Z",
     "iopub.status.busy": "2026-10-14T01:46:21.377972Z",
     "iopub.status.idle": "2026-10-14T01:46:21.383250Z",
     "shell.execute_reply": "2026-10-14T01:46:21.382337Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([1., 3., 5., 5.])"
      ]
     },
     "execution_count": 16,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "basis = BasisSHO(0, omega=1, nbas=4, dvr=True)\n",
    "# The harmonic oscillator Hamiltonian with the dimensionless x and p\n",
    "h_mat = 1/2 * omega * (basis.op_mat(\"p^2\") + basis.op_mat(\"x^2\"))\n",
    "np.linalg.eigvalsh(h_mat)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "9fcac33d-4bd5-4bbb-bff8-1eb87135267d",
   "metadata": {},
   "source": [
    "### `BasisSineDVR`\n",
    "`BasisSineDVR` is a basis based on particle-in-a-box. \n",
    "By default, `BasisSineDVR` is not a grid basis, because it uses the sin function as the basis, and the $x$ matrix is not diagonal. \n",
    "Set `dvr=True` such that the $x$ matrix becomes (approximately) diagonal.\n",
    "\n",
    "`BasisSineDVR` is best used with first-quantization and complicated nuclear potential.\n",
    "\n",
    "Usually, `BasisSineDVR` requires > 16 bases for reasonable numerical result. Note that usually you must carefully specify the initial state."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "id": "6b94de20-ce0d-4a2c-8485-37f5ab65947e",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-10-14T01:46:21.384805Z",
     "iopub.status.busy": "2026-10-14T01:46:21.384657Z",
     "iopub.status.idle": "2026-10-14T01:46:21.387918Z",
     "shell.execute_reply": "2026-10-14T01:46:21.387036Z"
    }
   },
   "outputs": [],
   "source": [
    "from renormalizer import BasisSineDVR\n",
    "# particle in a box. Range of grid is -3 to 3 with 16 grid points.\n",
    "basis = BasisSineDVR(0, nbas=16, xi=-3, xf=3, dvr=True)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "8ea667cc-abc0-4c68-8250-8a2f4be530d3",
   "metadata": {},
   "source": [
    "The grid points for the DVR basis can be accessed via `dvr_x`"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "id": "22bdd4dd-19a5-4c07-ae02-bc5087002d2c",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-10-14T01:46:21.389551Z",
     "iopub.status.busy": "2026-10-14T01:46:21.389382Z",
     "iopub.status.idle": "2026-10-14T01:46:21.393341Z",
     "shell.execute_reply": "2026-10-14T01:46:21.392537Z"
    },
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([-2.64705882, -2.29411765, -1.94117647, -1.58823529, -1.23529412,\n",
       "       -0.88235294, -0.52941176, -0.17647059,  0.17647059,  0.52941176,\n",
       "        0.88235294,  1.23529412,  1.58823529,  1.94117647,  2.29411765,\n",
       "        2.64705882])"
      ]
     },
     "execution_count": 18,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "basis.dvr_x"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "095f0269-5cfd-44c1-b614-a34445cfd2d8",
   "metadata": {},
   "source": [
    "The following cell numrically solves the quantum harmonic oscillator using `BasisSineDVR`"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "id": "4be72631-1f44-406a-8848-94ef439b3ebd",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-10-14T01:46:21.395196Z",
     "iopub.status.busy": "2026-10-14T01:46:21.395049Z",
     "iopub.status.idle": "2026-10-14T01:46:21.399880Z",
     "shell.execute_reply": "2026-10-14T01:46:21.398962Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ 1.00000014,  3.00000478,  5.00007562,  7.00073986,  9.00498407,\n",
       "       11.02437122, 13.0895611 , 15.25579691, 17.59098891, 20.15271789,\n",
       "       22.97765728, 26.07693738, 29.49028804, 33.14265301, 38.673214  ,\n",
       "       42.8094536 ])"
      ]
     },
     "execution_count": 19,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "h_mat = basis.op_mat(\"p^2\")/2 + 1/2 * omega** 2 * basis.op_mat(\"x^2\")\n",
    "np.linalg.eigvalsh(h_mat)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "486f1a27-e787-4a95-a090-fc4335e2f6ce",
   "metadata": {},
   "source": [
    "If the nuclear DoF is a harmonic oscillator, the following wavefunction should be put into the `condition` argument when initializing the ground state MPS.\n",
    "The default condition will set the wavefunction to a high-energy $\\delta$ function."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "id": "e2fe47d2-a21f-4ffa-9b52-edde39ec2cd2",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-10-14T01:46:21.401443Z",
     "iopub.status.busy": "2026-10-14T01:46:21.401296Z",
     "iopub.status.idle": "2026-10-14T01:46:21.405506Z",
     "shell.execute_reply": "2026-10-14T01:46:21.404597Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([-4.70136802e-04, -2.74685458e-03, -1.22547067e-02, -4.25908201e-02,\n",
       "       -1.15374089e-01, -2.43614258e-01, -4.00957667e-01, -5.14394732e-01,\n",
       "       -5.14394732e-01, -4.00957667e-01, -2.43614258e-01, -1.15374089e-01,\n",
       "       -4.25908201e-02, -1.22547067e-02, -2.74685458e-03, -4.70136802e-04])"
      ]
     },
     "execution_count": 20,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.linalg.eigh(h_mat)[1][:, 0]"
   ]
  }
 ],
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