.PhV Tutorium Gruppe 3.md

Jupyter-Notebooks zu den Tutorien in Physik V.

(PS: manchmal ist GitHub etwas überfordert mit der Vorschau der ganzen Notebooks — am Besten runterladen, oder im Binder anschauen!)

Tutorium 1.ipynb

Tutorium 10.ipynb

Tutorium 11.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Physik V Gruppe 3 — Tutorium #11\n",
    "\n",
    "> 18.01.2021         ralf@uni-bonn.de"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2021-01-28T10:04:08.677620Z",
     "iopub.status.busy": "2021-01-28T10:04:08.673819Z",
     "iopub.status.idle": "2021-01-28T10:04:08.731514Z",
     "shell.execute_reply": "2021-01-28T10:04:08.729517Z",
     "shell.execute_reply.started": "2021-01-28T10:04:08.677540Z"
    },
    "jupyter": {
     "source_hidden": true
    }
   },
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import astropy.units as u\n",
    "import astropy.constants as const\n",
    "\n",
    "import matplotlib.pyplot as plt\n",
    "import seaborn as sns\n",
    "sns.set_style(\"whitegrid\")\n",
    "\n",
    "import sympy as sy\n",
    "from uncertainties import ufloat, unumpy as unp\n",
    "\n",
    "u.c = u.def_unit('c', const.c)  # 'c' als Einheit\n",
    "\n",
    "m_e = const.m_e\n",
    "m_p = const.m_p\n",
    "m_n = const.m_n\n",
    "c = const.c\n",
    "hbar = const.hbar"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2021-01-28T10:04:08.963421Z",
     "iopub.status.busy": "2021-01-28T10:04:08.963190Z",
     "iopub.status.idle": "2021-01-28T10:04:08.999355Z",
     "shell.execute_reply": "2021-01-28T10:04:08.997059Z",
     "shell.execute_reply.started": "2021-01-28T10:04:08.963397Z"
    },
    "jupyter": {
     "source_hidden": true
    }
   },
   "outputs": [],
   "source": [
    "from IPython.display import display, Latex\n",
    "from IPython.core.magic import register_line_magic, needs_local_scope\n",
    "import re\n",
    "\n",
    "def _pretty(s):\n",
    "    \n",
    "    try:\n",
    "        # `import pint`\n",
    "        if isinstance(s, pint.quantity.Quantity):\n",
    "            return re.sub(r\"\\\\$\", \"\", f\"{s:.5~L}\")\n",
    "    except:\n",
    "        pass\n",
    "    try:\n",
    "        # `import sympy as sy`\n",
    "        if isinstance(s, sy.core.expr.Expr):\n",
    "            return sy.latex(s)\n",
    "    except:\n",
    "        pass\n",
    "    try:\n",
    "        # `import astropy.units as u`\n",
    "        if isinstance(s, (int, float)):\n",
    "            s = u.Quantity(s)\n",
    "        if isinstance(s, u.quantity.Quantity):\n",
    "            return s.to_string(format=\"latex\").lstrip(\"$\").rstrip(\"$\")\n",
    "    except Exception as e:\n",
    "        raise e\n",
    "        pass\n",
    "    \n",
    "    return str(s)\n",
    "\n",
    "def tex(*s, tag=\"align\", prefix=\"\", suffix=\"\"):\n",
    "    display(Latex(r\"\\begin{\"+tag+\"}\" +prefix+ \"\\n\"+ ' '.join(_pretty(e) for e in s) + \"\\n\" +suffix+ r\"\\end{\"+tag+\"}\"))\n",
    "\n",
    "@register_line_magic(\"tex\")\n",
    "@needs_local_scope\n",
    "def _tex(line, local_ns):\n",
    "    # TODO: handle single `<` and `>`\n",
    "    tex(re.sub(\"<(.*?)>\", lambda m: _pretty(eval(m.group(1))), line))\n",
    "\n",
    "@register_line_magic(\"tex-red\")\n",
    "@needs_local_scope\n",
    "def _tex_red(line, local_ns):\n",
    "    # TODO: handle single `<` and `>`\n",
    "    tex(re.sub(\"<(.*?)>\", lambda m: _pretty(eval(m.group(1))), line), prefix=r\"\\color{red}{\", suffix=\"}\")\n",
    "\n",
    "del _tex, _tex_red  # prevent conflicts in interactive session"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2020-12-01T20:40:34.034726Z",
     "iopub.status.busy": "2020-12-01T20:40:34.033935Z",
     "iopub.status.idle": "2020-12-01T20:40:34.045250Z",
     "shell.execute_reply": "2020-12-01T20:40:34.044175Z",
     "shell.execute_reply.started": "2020-12-01T20:40:34.034152Z"
    },
    "jupyter": {
     "source_hidden": true
    }
   },
   "source": [
    "(TeX Commands)\n",
    "\n",
    "$$\n",
    "\\let\\mjcolor\\color\n",
    "\\newcommand\\dv[2]{\\frac{\\mathrm d #1}{\\mathrm d #2}}\n",
    "\\newcommand\\sub[1]{_{\\text{#1}}}\n",
    "\\newcommand\\qqf{\\qquad\\mjcolor{red}{f}}\n",
    "\\newcommand\\qqok{\\qquad\\mjcolor{green}{\\checkmark}}\n",
    "$$"
   ]
  },
  {
   "attachments": {
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"
    }
   },
   "cell_type": "markdown",
   "metadata": {
    "jupyter": {
     "source_hidden": true
    }
   },
   "source": [
    "## Äquivalenzen\n",
    "\n",
    "\n",
    "![att](attachment:ac424160-6059-446b-bc0c-f1352cccd2a9.png)\n",
    "\n",
    "\n",
    "<!--\n",
    "\n",
    "% erstellt mit LaTeXiT\n",
    "\n",
    "\\documentclass[10pt]{article}\n",
    "\\usepackage[usenames]{color}\n",
    "\\usepackage{amssymb}\n",
    "\\usepackage{amsmath}\n",
    "\\usepackage{booktabs}\n",
    "\\usepackage{siunitx}\n",
    "\\linespread{1.05}\n",
    "\\usepackage[T1]{fontenc}\n",
    "\\usepackage[utf8]{inputenc}\n",
    "\n",
    "\n",
    "%------------------------------------------------\n",
    "\n",
    "\n",
    "\\begin{tabular}{ls[table-unit-alignment = left] \n",
    "ls[table-unit-alignment = left] \n",
    "}\n",
    "\\toprule\n",
    "& {\\textbf{SI}} & \\textbf{Faktor} &\n",
    "{\\textbf{nat.}}\n",
    "\\\\ \n",
    "\\midrule\n",
    "Masse & kg & $c^2$ & GeV \\\\\n",
    "Länge & m & $(\\hbar c)^{-1}$ & GeV^{-1} \\\\\n",
    "Zeit & s & $\\hbar^{-1}$ & GeV^{-1} \\\\ \n",
    "Energie & kg.m.s^{-2} & $1$ & GeV\\\\ \n",
    "\\bottomrule\n",
    "\\end{tabular}\n",
    "\n",
    "-->"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## B11-H1. Lebensdauer des Tau-Leptons"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### a)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2021-01-28T10:04:24.547723Z",
     "iopub.status.busy": "2021-01-28T10:04:24.547347Z",
     "iopub.status.idle": "2021-01-28T10:04:24.553278Z",
     "shell.execute_reply": "2021-01-28T10:04:24.552227Z",
     "shell.execute_reply.started": "2021-01-28T10:04:24.547682Z"
    }
   },
   "outputs": [],
   "source": [
    "m_mu = 105.7 * u.MeV\n",
    "tau_mu = 2.2e-6 * u.s\n",
    "m_tau = 1.78 * u.GeV"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Kürzen des Bruchs mit `sympy`**"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2021-01-28T10:04:46.108684Z",
     "iopub.status.busy": "2021-01-28T10:04:46.107556Z",
     "iopub.status.idle": "2021-01-28T10:04:46.117732Z",
     "shell.execute_reply": "2021-01-28T10:04:46.116700Z",
     "shell.execute_reply.started": "2021-01-28T10:04:46.108636Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.005208333333333333"
      ]
     },
     "execution_count": 23,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "64 / (2 * 12 * 512)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2021-01-28T10:05:48.485360Z",
     "iopub.status.busy": "2021-01-28T10:05:48.485118Z",
     "iopub.status.idle": "2021-01-28T10:05:48.491514Z",
     "shell.execute_reply": "2021-01-28T10:05:48.490505Z",
     "shell.execute_reply.started": "2021-01-28T10:05:48.485335Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle \\frac{1}{3}$"
      ],
      "text/plain": [
       "1/3"
      ]
     },
     "execution_count": 28,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "sy.Rational(3,9)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2021-01-28T10:06:45.785821Z",
     "iopub.status.busy": "2021-01-28T10:06:45.785363Z",
     "iopub.status.idle": "2021-01-28T10:06:45.792181Z",
     "shell.execute_reply": "2021-01-28T10:06:45.791201Z",
     "shell.execute_reply.started": "2021-01-28T10:06:45.785791Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle \\frac{1}{192 \\pi^{3}}$"
      ],
      "text/plain": [
       "1/(192*pi**3)"
      ]
     },
     "execution_count": 31,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "sy.Rational(64) / (2 * 12 * (8*sy.pi)**3)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Lebensdauer τ**"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2021-01-28T10:07:20.653688Z",
     "iopub.status.busy": "2021-01-28T10:07:20.653402Z",
     "iopub.status.idle": "2021-01-28T10:07:20.662014Z",
     "shell.execute_reply": "2021-01-28T10:07:20.661451Z",
     "shell.execute_reply.started": "2021-01-28T10:07:20.653661Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/latex": [
       "\\begin{align}\n",
       "\\tau_\\tau = 2.9239511 \\times 10^{-13} \\; \\mathrm{s}\n",
       "\\end{align}"
      ],
      "text/plain": [
       "<IPython.core.display.Latex object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/latex": [
       "\\begin{align}\n",
       "\\text{PDG:}\\quad \\tau_\\tau = 2.903\\pm0.005\\times10^{-13}\\,\\text{s}\n",
       "\\end{align}"
      ],
      "text/plain": [
       "<IPython.core.display.Latex object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "tau_tau = (0.18 * tau_mu * (m_mu / m_tau)**5).decompose()\n",
    "%tex \\tau_\\tau = <tau_tau>\n",
    "%tex \\text{PDG:}\\quad \\tau_\\tau = 2.903\\pm0.005\\times10^{-13}\\,\\text{s}"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## B11-H2. Cabbibo-Mischungswinkel in β⁻- und Hadron-Zerfällen"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### a)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2021-01-28T10:31:44.909395Z",
     "iopub.status.busy": "2021-01-28T10:31:44.909163Z",
     "iopub.status.idle": "2021-01-28T10:31:44.913993Z",
     "shell.execute_reply": "2021-01-28T10:31:44.912907Z",
     "shell.execute_reply.started": "2021-01-28T10:31:44.909371Z"
    }
   },
   "outputs": [],
   "source": [
    "GF_mu = 1.1638e-5 * u.GeV**-2\n",
    "GF_beta = 1.1361e-5 *u.GeV**-2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2021-01-28T10:31:49.191794Z",
     "iopub.status.busy": "2021-01-28T10:31:49.191553Z",
     "iopub.status.idle": "2021-01-28T10:31:49.198053Z",
     "shell.execute_reply": "2021-01-28T10:31:49.197054Z",
     "shell.execute_reply.started": "2021-01-28T10:31:49.191745Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/latex": [
       "\\begin{align}\n",
       "\\theta_c = 0.21861547 \\; \\mathrm{rad} = 12.525744 \\; \\mathrm{{}^{\\circ}}\n",
       "\\end{align}"
      ],
      "text/plain": [
       "<IPython.core.display.Latex object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "theta_c = np.arccos(GF_beta / GF_mu)\n",
    "%tex \\theta_c = <theta_c> = <theta_c.to(\"deg\")>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "3.8.5 (Framework)",
   "language": "python",
   "name": "3.8.5-framework"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.8.5"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 4
}

Tutorium 12.ipynb

Tutorium 13.ipynb

Tutorium 3.ipynb

Tutorium 4.ipynb

Tutorium 5.ipynb

environment.yml

Tutorium 6.ipynb

Tutorium 8.ipynb