From 67d004651fe400719d7748a2edc2d4f3cf546bca Mon Sep 17 00:00:00 2001
From: Morten Hjorth-Jensen <morten.hjorth-jensen@fys.uio.no>
Date: Thu, 17 Oct 2024 12:42:08 +0200
Subject: [PATCH] added video

---
 doc/pub/week42/html/week42-bs.html            |   5 +-
 doc/pub/week42/html/week42-reveal.html        |   7 +-
 doc/pub/week42/html/week42-solarized.html     |   5 +-
 doc/pub/week42/html/week42.html               |   5 +-
 .../week42-checkpoint.ipynb                   | 977 ++++++++++++++++++
 doc/pub/week42/ipynb/ipynb-week42-src.tar.gz  | Bin 191 -> 192 bytes
 doc/pub/week42/ipynb/week42.ipynb             | 177 ++--
 doc/pub/week42/pdf/week42.pdf                 | Bin 259896 -> 293104 bytes
 doc/src/week42/week42.do.txt                  |   3 +-
 9 files changed, 1083 insertions(+), 96 deletions(-)
 create mode 100644 doc/pub/week42/ipynb/.ipynb_checkpoints/week42-checkpoint.ipynb

diff --git a/doc/pub/week42/html/week42-bs.html b/doc/pub/week42/html/week42-bs.html
index 6fd0c677..cb582711 100644
--- a/doc/pub/week42/html/week42-bs.html
+++ b/doc/pub/week42/html/week42-bs.html
@@ -200,8 +200,9 @@ <h2 id="week-42-october-14-18-2024" class="anchor">Week 42, October 14-18, 2024
 <ul>
   <li> The first lecture is about the finalization of the calculation of the ground state energy of the homogeneous electron gas in three dimensions</li>
   <li> Start discussion of density functional theory</li>
-  <li> Discussions of first midterm
-<!-- * <a href="https://youtu.be/" target="_self">Video of lecture TBA</a> --></li>
+  <li> Discussions of first midterm</li>
+  <li> Video of lecture at <a href="https://youtu.be/VbLlyZYRnYg" target="_self"><tt>https://youtu.be/VbLlyZYRnYg</tt></a></li>
+  <li> Whiteboard notes at <a href="https://github.com/ManyBodyPhysics/FYS4480/blob/master/doc/HandwrittenNotes/2024/NotesOctober17.pdf" target="_self"><tt>https://github.com/ManyBodyPhysics/FYS4480/blob/master/doc/HandwrittenNotes/2024/NotesOctober17.pdf</tt></a></li>  
 </ul>
 <li> Friday:</li>
 <ul>
diff --git a/doc/pub/week42/html/week42-reveal.html b/doc/pub/week42/html/week42-reveal.html
index 31153c67..76994e10 100644
--- a/doc/pub/week42/html/week42-reveal.html
+++ b/doc/pub/week42/html/week42-reveal.html
@@ -209,8 +209,11 @@ <h2 id="week-42-october-14-18-2024">Week 42, October 14-18, 2024 </h2>
 
 <p><li> Start discussion of density functional theory</li>
 
-<p><li> Discussions of first midterm
-<!-- * <a href="https://youtu.be/" target="_blank">Video of lecture TBA</a> --></li>
+<p><li> Discussions of first midterm</li>
+
+<p><li> Video of lecture at <a href="https://youtu.be/VbLlyZYRnYg" target="_blank"><tt>https://youtu.be/VbLlyZYRnYg</tt></a></li>
+
+<p><li> Whiteboard notes at <a href="https://github.com/ManyBodyPhysics/FYS4480/blob/master/doc/HandwrittenNotes/2024/NotesOctober17.pdf" target="_blank"><tt>https://github.com/ManyBodyPhysics/FYS4480/blob/master/doc/HandwrittenNotes/2024/NotesOctober17.pdf</tt></a></li>  
 </ul>
 <p>
 <p><li> Friday:</li>
diff --git a/doc/pub/week42/html/week42-solarized.html b/doc/pub/week42/html/week42-solarized.html
index 4a5dc094..309e6540 100644
--- a/doc/pub/week42/html/week42-solarized.html
+++ b/doc/pub/week42/html/week42-solarized.html
@@ -172,8 +172,9 @@ <h2 id="week-42-october-14-18-2024">Week 42, October 14-18, 2024 </h2>
 <ul>
   <li> The first lecture is about the finalization of the calculation of the ground state energy of the homogeneous electron gas in three dimensions</li>
   <li> Start discussion of density functional theory</li>
-  <li> Discussions of first midterm
-<!-- * <a href="https://youtu.be/" target="_blank">Video of lecture TBA</a> --></li>
+  <li> Discussions of first midterm</li>
+  <li> Video of lecture at <a href="https://youtu.be/VbLlyZYRnYg" target="_blank"><tt>https://youtu.be/VbLlyZYRnYg</tt></a></li>
+  <li> Whiteboard notes at <a href="https://github.com/ManyBodyPhysics/FYS4480/blob/master/doc/HandwrittenNotes/2024/NotesOctober17.pdf" target="_blank"><tt>https://github.com/ManyBodyPhysics/FYS4480/blob/master/doc/HandwrittenNotes/2024/NotesOctober17.pdf</tt></a></li>  
 </ul>
 <li> Friday:</li>
 <ul>
diff --git a/doc/pub/week42/html/week42.html b/doc/pub/week42/html/week42.html
index 696e5327..3cd15f7b 100644
--- a/doc/pub/week42/html/week42.html
+++ b/doc/pub/week42/html/week42.html
@@ -249,8 +249,9 @@ <h2 id="week-42-october-14-18-2024">Week 42, October 14-18, 2024 </h2>
 <ul>
   <li> The first lecture is about the finalization of the calculation of the ground state energy of the homogeneous electron gas in three dimensions</li>
   <li> Start discussion of density functional theory</li>
-  <li> Discussions of first midterm
-<!-- * <a href="https://youtu.be/" target="_blank">Video of lecture TBA</a> --></li>
+  <li> Discussions of first midterm</li>
+  <li> Video of lecture at <a href="https://youtu.be/VbLlyZYRnYg" target="_blank"><tt>https://youtu.be/VbLlyZYRnYg</tt></a></li>
+  <li> Whiteboard notes at <a href="https://github.com/ManyBodyPhysics/FYS4480/blob/master/doc/HandwrittenNotes/2024/NotesOctober17.pdf" target="_blank"><tt>https://github.com/ManyBodyPhysics/FYS4480/blob/master/doc/HandwrittenNotes/2024/NotesOctober17.pdf</tt></a></li>  
 </ul>
 <li> Friday:</li>
 <ul>
diff --git a/doc/pub/week42/ipynb/.ipynb_checkpoints/week42-checkpoint.ipynb b/doc/pub/week42/ipynb/.ipynb_checkpoints/week42-checkpoint.ipynb
new file mode 100644
index 00000000..1e8d1efd
--- /dev/null
+++ b/doc/pub/week42/ipynb/.ipynb_checkpoints/week42-checkpoint.ipynb
@@ -0,0 +1,977 @@
+{
+ "cells": [
+  {
+   "cell_type": "markdown",
+   "id": "a1961317",
+   "metadata": {},
+   "source": [
+    "<!-- HTML file automatically generated from DocOnce source (https://github.com/doconce/doconce/)\n",
+    "doconce format html week42.do.txt --no_mako -->\n",
+    "<!-- dom:TITLE: Week 42: Hartree-Fock theory in second quantization and diagrammatic representation. Stability of Hartree-Fock theory -->"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "0d9036fe",
+   "metadata": {},
+   "source": [
+    "# Week 42: Hartree-Fock theory in second quantization and diagrammatic representation. Stability of Hartree-Fock theory\n",
+    "**Morten Hjorth-Jensen**, Department of Physics and Center for Computing in Science Education, University of Oslo, Norway and Department of Physics and Astronomy and Facility for Rare Isotope Beams, Michigan State University, USA\n",
+    "\n",
+    "Date: **October 14-18**\n",
+    "\n",
+    "<!-- todo: add material about the calculation of the HEG -->\n",
+    "<!-- add material about DFT -->"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "ac9563ab",
+   "metadata": {},
+   "source": [
+    "## Week 42, October 14-18, 2024\n",
+    "**Topics to be covered.**\n",
+    "\n",
+    "1. Thursday:\n",
+    "\n",
+    "  * The first lecture is about the finalization of the calculation of the ground state energy of the homogeneous electron gas in three dimensions\n",
+    "\n",
+    "  * Start discussion of density functional theory\n",
+    "\n",
+    "  * Discussions of first midterm\n",
+    "<!-- * [Video of lecture TBA](https://youtu.be/) -->\n",
+    "\n",
+    "2. Friday:\n",
+    "\n",
+    "  * Density functional theory\n",
+    "\n",
+    "  * Discussions of  first midterm\n",
+    "\n",
+    "* Lecture Material: These slides and handwritten notes\n",
+    "\n",
+    "* First midterm set at <https://github.com/ManyBodyPhysics/FYS4480/blob/master/doc/Exercises/2024/FirstMidterm2024.pdf>"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "5f6f1b3b",
+   "metadata": {},
+   "source": [
+    "## Hartree-Fock ground state energy for the  electron gas in three dimensions\n",
+    "\n",
+    "We consider a system of electrons in infinite matter, the so-called electron gas. This is a homogeneous system and the one-particle states are given by plane wave function normalized to a volume $V$ \n",
+    "for a box with length $L$ (the limit $L\\rightarrow \\infty$ is to be taken after we have computed various expectation values)"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "921a9430",
+   "metadata": {},
+   "source": [
+    "$$\n",
+    "\\psi_{\\mathbf{k}\\sigma}(\\mathbf{r})= \\frac{1}{\\sqrt{V}}\\exp{(i\\mathbf{kr})}\\xi_{\\sigma}\n",
+    "$$"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "75e046ff",
+   "metadata": {},
+   "source": [
+    "where $\\mathbf{k}$ is the wave number and  $\\xi_{\\sigma}$ is a spin function for either spin up or down"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "6b1e6caa",
+   "metadata": {},
+   "source": [
+    "$$\n",
+    "\\xi_{\\sigma=+1/2}=\\left(\\begin{array}{c} 1 \\\\ 0 \\end{array}\\right) \\hspace{0.5cm}\n",
+    "\\xi_{\\sigma=-1/2}=\\left(\\begin{array}{c} 0 \\\\ 1 \\end{array}\\right).\n",
+    "$$"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "759f2763",
+   "metadata": {},
+   "source": [
+    "## Periodic boundary conditions\n",
+    "\n",
+    "We assume that we have periodic boundary conditions which limit the allowed wave numbers to"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "32d53cdf",
+   "metadata": {},
+   "source": [
+    "$$\n",
+    "k_i=\\frac{2\\pi n_i}{L}\\hspace{0.5cm} i=x,y,z \\hspace{0.5cm} n_i=0,\\pm 1,\\pm 2, \\dots\n",
+    "$$"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "fcb183ae",
+   "metadata": {},
+   "source": [
+    "We assume first that the particles interact via a central, symmetric and translationally invariant\n",
+    "interaction  $V(r_{12})$ with\n",
+    "$r_{12}=|\\mathbf{r}_1-\\mathbf{r}_2|$.  The interaction is spin independent."
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "60ecada4",
+   "metadata": {},
+   "source": [
+    "## Total Hamiltonian\n",
+    "\n",
+    "The total Hamiltonian consists then of kinetic and potential energy"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "a626f774",
+   "metadata": {},
+   "source": [
+    "$$\n",
+    "\\hat{H} = \\hat{T}+\\hat{V}.\n",
+    "$$"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "d2a6bb9f",
+   "metadata": {},
+   "source": [
+    "The operator for the kinetic energy is given by"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "7560b068",
+   "metadata": {},
+   "source": [
+    "$$\n",
+    "\\hat{T}=\\sum_{\\mathbf{k}\\sigma}\\frac{\\hbar^2k^2}{2m}a_{\\mathbf{k}\\sigma}^{\\dagger}a_{\\mathbf{k}\\sigma}.\n",
+    "$$"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "aea9481c",
+   "metadata": {},
+   "source": [
+    "## Exercise 1: Express interaction using creation and annihilation operators\n",
+    "\n",
+    "Find the expression for the interaction\n",
+    "$\\hat{V}$ expressed with creation and annihilation operators.\n",
+    "\n",
+    "The expression for the interaction\n",
+    "has to be written in  $k$ space, even though $V$ depends only on the relative distance. It means that you need to set up the Fourier transform $\\langle \\mathbf{k}_i\\mathbf{k}_j| V | \\mathbf{k}_m\\mathbf{k}_n\\rangle$.\n",
+    "\n",
+    "A general two-body interaction element is given by (not using anti-symmetrized matrix elements)"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "db7541d1",
+   "metadata": {},
+   "source": [
+    "$$\n",
+    "\\hat{V} = \\frac{1}{2} \\sum_{pqrs} \\langle pq \\hat{v} \\vert rs\\rangle a_p^\\dagger a_q^\\dagger a_s a_r ,\n",
+    "$$"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "cfa8f577",
+   "metadata": {},
+   "source": [
+    "where $\\hat{v}$ is assumed to depend only on the relative distance between two interacting particles, that is\n",
+    "$\\hat{v} = v(\\vec r_1, \\vec r_2) = v(|\\vec r_1 - \\vec r_2|) = v(r)$, with $r = |\\vec r_1 - \\vec r_2|$)."
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "4e591170",
+   "metadata": {},
+   "source": [
+    "## With spin degrees of freedom\n",
+    "\n",
+    "In our case we have, writing out explicitely the spin degrees of freedom as well"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "e67ff404",
+   "metadata": {},
+   "source": [
+    "<!-- Equation labels as ordinary links -->\n",
+    "<div id=\"_auto1\"></div>\n",
+    "\n",
+    "$$\n",
+    "\\begin{equation}\n",
+    "\\hat{V} = \\frac{1}{2} \\sum_{\\substack{\\sigma_p \\sigma_q \\\\ \\sigma_r \\sigma_s}}\n",
+    "\\sum_{\\substack{\\mathbf{k}_p \\mathbf{k}_q \\\\ \\mathbf{k}_r \\mathbf{k}_s}}\n",
+    "\\langle \\mathbf{k}_p \\sigma_p, \\mathbf{k}_q \\sigma_2\\vert v \\vert \\mathbf{k}_r \\sigma_3, \\mathbf{k}_s \\sigma_s\\rangle\n",
+    "a_{\\mathbf{k}_p \\sigma_p}^\\dagger a_{\\mathbf{k}_q \\sigma_q}^\\dagger a_{\\mathbf{k}_s \\sigma_s} a_{\\mathbf{k}_r \\sigma_r} .\n",
+    "\\label{_auto1} \\tag{1}\n",
+    "\\end{equation}\n",
+    "$$"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "c95801fb",
+   "metadata": {},
+   "source": [
+    "## Plane waves\n",
+    "\n",
+    "Inserting plane waves as eigenstates we can rewrite the matrix element as"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "b1f2a9bc",
+   "metadata": {},
+   "source": [
+    "$$\n",
+    "\\langle \\mathbf{k}_p \\sigma_p, \\mathbf{k}_q \\sigma_q\\vert \\hat{v} \\vert \\mathbf{k}_r \\sigma_r, \\mathbf{k}_s \\sigma_s\\rangle =\n",
+    "\\frac{1}{V^2} \\delta_{\\sigma_p \\sigma_r} \\delta_{\\sigma_q \\sigma_s}\n",
+    "\\int\\int \\exp{-i(\\mathbf{k}_p \\cdot \\mathbf{r}_p)} \\exp{-i( \\mathbf{k}_q \\cdot \\mathbf{r}_q)} \\hat{v}(r) \\exp{i(\\mathbf{k}_r \\cdot \\mathbf{r}_p)} \\exp{i( \\mathbf{k}_s \\cdot \\mathbf{r}_q)} d\\mathbf{r}_p d\\mathbf{r}_q ,\n",
+    "$$"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "0f02f04f",
+   "metadata": {},
+   "source": [
+    "where we have used the orthogonality properties of the spin functions. We change now the variables of integration\n",
+    "by defining $\\mathbf{r} = \\mathbf{r}_p - \\mathbf{r}_q$, which gives $\\mathbf{r}_p = \\mathbf{r} + \\mathbf{r}_q$ and $d^3 \\mathbf{r} = d^3 \\mathbf{r}_p$."
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "575eee27",
+   "metadata": {},
+   "source": [
+    "## Integration limits\n",
+    "\n",
+    "The limits are not changed since they are from $-\\infty$ to  $\\infty$ for all integrals. This results in"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "eaf066a2",
+   "metadata": {},
+   "source": [
+    "$$\n",
+    "\\begin{align*}\n",
+    "\\langle \\mathbf{k}_p \\sigma_p, \\mathbf{k}_q \\sigma_q\\vert \\hat{v} \\vert \\mathbf{k}_r \\sigma_r, \\mathbf{k}_s \\sigma_s\\rangle\n",
+    "&= \\frac{1}{V^2} \\delta_{\\sigma_p \\sigma_r} \\delta_{\\sigma_q \\sigma_s} \\int\\exp{i (\\mathbf{k}_s - \\mathbf{k}_q) \\cdot \\mathbf{r}_q} \\int v(r) \\exp{i(\\mathbf{k}_r - \\mathbf{k}_p) \\cdot ( \\mathbf{r} + \\mathbf{r}_q)} d\\mathbf{r} d\\mathbf{r}_q \\\\\n",
+    "&= \\frac{1}{V^2} \\delta_{\\sigma_p \\sigma_r} \\delta_{\\sigma_q \\sigma_s} \\int v(r) \\exp{i\\left[(\\mathbf{k}_r - \\mathbf{k}_p) \\cdot \\mathbf{r}\\right]}\n",
+    "\\int \\exp{i\\left[(\\mathbf{k}_s - \\mathbf{k}_q + \\mathbf{k}_r - \\mathbf{k}_p) \\cdot \\mathbf{r}_q\\right]} d\\mathbf{r}_q d\\mathbf{r} .\n",
+    "\\end{align*}\n",
+    "$$"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "7e8f7a5e",
+   "metadata": {},
+   "source": [
+    "## Recognizing integral\n",
+    "\n",
+    "We recognize the integral over $\\mathbf{r}_q$ as a $\\delta$-function, resulting in"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "844f1feb",
+   "metadata": {},
+   "source": [
+    "$$\n",
+    "\\langle \\mathbf{k}_p \\sigma_p, \\mathbf{k}_q \\sigma_q\\vert \\hat{v} \\vert \\mathbf{k}_r \\sigma_r, \\mathbf{k}_s \\sigma_s\\rangle =\n",
+    "\\frac{1}{V} \\delta_{\\sigma_p \\sigma_r} \\delta_{\\sigma_q \\sigma_s} \\delta_{(\\mathbf{k}_p + \\mathbf{k}_q),(\\mathbf{k}_r + \\mathbf{k}_s)} \\int v(r) \\exp{i\\left[(\\mathbf{k}_r - \\mathbf{k}_p) \\cdot \\mathbf{r}\\right]} d^3r .\n",
+    "$$"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "b6a216ee",
+   "metadata": {},
+   "source": [
+    "For this equation to be different from zero, we must have conservation of momenta, we need to satisfy\n",
+    "$\\mathbf{k}_p + \\mathbf{k}_q = \\mathbf{k}_r + \\mathbf{k}_s$."
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "a9c2b17c",
+   "metadata": {},
+   "source": [
+    "## Conservation of momentum\n",
+    "\n",
+    "We can use the conservation of momenta to remove one of the summation variables resulting in"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "d0d7e74d",
+   "metadata": {},
+   "source": [
+    "$$\n",
+    "\\hat{V} =\n",
+    "\\frac{1}{2V} \\sum_{\\sigma \\sigma'} \\sum_{\\mathbf{k}_p \\mathbf{k}_q \\mathbf{k}_r} \\left[ \\int v(r) \\exp{i\\left[(\\mathbf{k}_r - \\mathbf{k}_p) \\cdot \\mathbf{r}\\right]} d^3r \\right]\n",
+    "a_{\\mathbf{k}_p \\sigma}^\\dagger a_{\\mathbf{k}_q \\sigma'}^\\dagger a_{\\mathbf{k}_p + \\mathbf{k}_q - \\mathbf{k}_r, \\sigma'} a_{\\mathbf{k}_r \\sigma},\n",
+    "$$"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "d205980a",
+   "metadata": {},
+   "source": [
+    "which can be rewritten as"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "e255991a",
+   "metadata": {},
+   "source": [
+    "<!-- Equation labels as ordinary links -->\n",
+    "<div id=\"eq:V\"></div>\n",
+    "\n",
+    "$$\n",
+    "\\begin{equation}\n",
+    "\\hat{V} =\n",
+    "\\frac{1}{2V} \\sum_{\\sigma \\sigma'} \\sum_{\\mathbf{k} \\mathbf{p} \\mathbf{q}} \\left[ \\int v(r) \\exp{-i( \\mathbf{q} \\cdot \\mathbf{r})} d\\mathbf{r} \\right]\n",
+    "a_{\\mathbf{k} + \\mathbf{q}, \\sigma}^\\dagger a_{\\mathbf{p} - \\mathbf{q}, \\sigma'}^\\dagger a_{\\mathbf{p} \\sigma'} a_{\\mathbf{k} \\sigma},\n",
+    "\\label{eq:V} \\tag{2}\n",
+    "\\end{equation}\n",
+    "$$"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "7321d5cb",
+   "metadata": {},
+   "source": [
+    "## Some definitions\n",
+    "\n",
+    "In the last equation we defined\n",
+    "the quantities\n",
+    "$\\mathbf{p} = \\mathbf{k}_p + \\mathbf{k}_q - \\mathbf{k}_r$, $\\mathbf{k} = \\mathbf{k}_r$ og $\\mathbf{q} = \\mathbf{k}_p - \\mathbf{k}_r$."
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "31033161",
+   "metadata": {},
+   "source": [
+    "## Reference energy\n",
+    "\n",
+    "Let us now compute the expectation value of the reference energy using the expressions for the kinetic energy operator and the interaction.\n",
+    "We need to compute $\\langle \\Phi_0\\vert \\hat{H} \\vert \\Phi_0\\rangle = \\langle \\Phi_0\\vert \\hat{T} \\vert \\Phi_0\\rangle + \\langle \\Phi_0\\vert \\hat{V} \\vert \\Phi_0\\rangle$, where $\\vert \\Phi_0\\rangle$ is our reference Slater determinant, constructed from filling all single-particle states up to the Fermi level.\n",
+    "Let us start with the kinetic energy first"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "8e97f708",
+   "metadata": {},
+   "source": [
+    "$$\n",
+    "\\langle \\Phi_0\\vert \\hat{T} \\vert \\Phi_0\\rangle \n",
+    "= \\langle \\Phi_0\\vert \\left( \\sum_{\\mathbf{p} \\sigma} \\frac{\\hbar^2 p^2}{2m} a_{\\mathbf{p} \\sigma}^\\dagger a_{\\mathbf{p} \\sigma} \\right) \\vert \\Phi_0\\rangle\n",
+    "= \\sum_{\\mathbf{p} \\sigma} \\frac{\\hbar^2 p^2}{2m} \\langle \\Phi_0\\vert a_{\\mathbf{p} \\sigma}^\\dagger a_{\\mathbf{p} \\sigma} \\vert \\Phi_0\\rangle .\n",
+    "$$"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "193ce141",
+   "metadata": {},
+   "source": [
+    "## Kinetic  energy\n",
+    "\n",
+    "From the possible contractions using Wick's theorem, it is straightforward to convince oneself that the expression for the kinetic energy becomes"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "81188efb",
+   "metadata": {},
+   "source": [
+    "$$\n",
+    "\\langle \\Phi_0\\vert \\hat{T} \\vert \\Phi_0\\rangle = \\sum_{\\mathbf{i} \\leq F} \\frac{\\hbar^2 k_i^2}{m} = \\frac{V}{(2\\pi)^3} \\frac{\\hbar^2}{m} \\int_0^{k_F} k^2 d\\mathbf{k}.\n",
+    "$$"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "55af2b83",
+   "metadata": {},
+   "source": [
+    "The sum of the spin degrees of freedom results in  a factor of two only if we deal with identical spin $1/2$ fermions. \n",
+    "Changing to spherical coordinates, the integral over the momenta $k$ results in the final expression"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "e9f2ab1a",
+   "metadata": {},
+   "source": [
+    "$$\n",
+    "\\langle \\Phi_0\\vert \\hat{T} \\vert \\Phi_0\\rangle = \\frac{V}{(2\\pi)^3} \\left( 4\\pi \\int_0^{k_F} k^4 d\\mathbf{k} \\right) = \\frac{4\\pi V}{(2\\pi)^3} \\frac{1}{5} k_F^5 = \\frac{4\\pi V}{5(2\\pi)^3} k_F^5 = \\frac{\\hbar^2 V}{10\\pi^2 m} k_F^5 .\n",
+    "$$"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "f4433345",
+   "metadata": {},
+   "source": [
+    "## Density of states\n",
+    "\n",
+    "The density of states in momentum space is given by $2V/(2\\pi)^3$, where we have included the degeneracy due to the spin degrees of freedom.\n",
+    "The volume is given by  $4\\pi k_F^3/3$, and the number of particles becomes"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "5c262a8e",
+   "metadata": {},
+   "source": [
+    "$$\n",
+    "N = \\frac{2V}{(2\\pi)^3} \\frac{4}{3} \\pi k_F^3 = \\frac{V}{3\\pi^2} k_F^3 \\quad \\Rightarrow \\quad\n",
+    "k_F = \\left( \\frac{3\\pi^2 N}{V} \\right)^{1/3}.\n",
+    "$$"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "54394492",
+   "metadata": {},
+   "source": [
+    "This gives us"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "0bc41015",
+   "metadata": {},
+   "source": [
+    "<!-- Equation labels as ordinary links -->\n",
+    "<div id=\"eq:T_forventning\"></div>\n",
+    "\n",
+    "$$\n",
+    "\\begin{equation}\n",
+    "\\langle \\Phi_0\\vert \\hat{T} \\vert \\Phi_0\\rangle =\n",
+    "\\frac{\\hbar^2 V}{10\\pi^2 m} \\left( \\frac{3\\pi^2 N}{V} \\right)^{5/3} =\n",
+    "\\frac{\\hbar^2 (3\\pi^2)^{5/3} N}{10\\pi^2 m} \\rho^{2/3} ,\n",
+    "\\label{eq:T_forventning} \\tag{3}\n",
+    "\\end{equation}\n",
+    "$$"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "1e1ee5cb",
+   "metadata": {},
+   "source": [
+    "## Potential energy\n",
+    "\n",
+    "We are now ready to calculate the expectation value of the potential energy"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "48831c8e",
+   "metadata": {},
+   "source": [
+    "$$\n",
+    "\\begin{align*}\n",
+    "\\langle \\Phi_0\\vert \\hat{V} \\vert \\Phi_0\\rangle \n",
+    "&= \\langle \\Phi_0\\vert \\left( \\frac{1}{2V} \\sum_{\\sigma \\sigma'} \\sum_{\\mathbf{k} \\mathbf{p} \\mathbf{q} } \\left[ \\int v(r) \\exp{-i (\\mathbf{q} \\cdot \\mathbf{r})} d\\mathbf{r} \\right] a_{\\mathbf{k} + \\mathbf{q}, \\sigma}^\\dagger a_{\\mathbf{p} - \\mathbf{q}, \\sigma'}^\\dagger a_{\\mathbf{p} \\sigma'} a_{\\mathbf{k} \\sigma} \\right) \\vert \\Phi_0\\rangle \\\\\n",
+    "&= \\frac{1}{2V} \\sum_{\\sigma \\sigma'} \\sum_{\\mathbf{k} \\mathbf{p} \\mathbf{q}} \\left[ \\int v(r) \\exp{-i (\\mathbf{q} \\cdot \\mathbf{r})} d\\mathbf{r} \\right]\\langle \\Phi_0\\vert a_{\\mathbf{k} + \\mathbf{q}, \\sigma}^\\dagger a_{\\mathbf{p} - \\mathbf{q}, \\sigma'}^\\dagger a_{\\mathbf{p} \\sigma'} a_{\\mathbf{k} \\sigma} \\vert \\Phi_0\\rangle .\n",
+    "\\end{align*}\n",
+    "$$"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "6a41dad3",
+   "metadata": {},
+   "source": [
+    "## Non-zero term\n",
+    "\n",
+    "The only contractions which result in non-zero results are those that involve states below the Fermi level, that is \n",
+    "$k \\leq k_F$, $p \\leq k_F$, $|\\mathbf{p} - \\mathbf{q}| < \\mathbf{k}_F$ and $|\\mathbf{k} + \\mathbf{q}| \\leq k_F$. Due to momentum conservation we must also have $\\mathbf{k} + \\mathbf{q} = \\mathbf{p}$, $\\mathbf{p} - \\mathbf{q} = \\mathbf{k}$ and  $\\sigma = \\sigma'$ or  $\\mathbf{k} + \\mathbf{q} = \\mathbf{k}$ and $\\mathbf{p} - \\mathbf{q} = \\mathbf{p}$. \n",
+    "Summarizing, we must have"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "f07e1119",
+   "metadata": {},
+   "source": [
+    "$$\n",
+    "\\mathbf{k} + \\mathbf{q} = \\mathbf{p} \\quad \\text{and} \\quad \\sigma = \\sigma', \\qquad\n",
+    "\\text{or} \\qquad\n",
+    "\\mathbf{q} = \\mathbf{0} .\n",
+    "$$"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "5b629eac",
+   "metadata": {},
+   "source": [
+    "## Direct and exchange terms\n",
+    "\n",
+    "We obtain then"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "d6eb81f0",
+   "metadata": {},
+   "source": [
+    "$$\n",
+    "\\langle \\Phi_0\\vert \\hat{V} \\vert \\Phi_0\\rangle =\n",
+    "\\frac{1}{2V} \\left( \\sum_{\\sigma \\sigma'} \\sum_{\\mathbf{q} \\mathbf{p} \\leq F} \\left[ \\int v(r) d\\mathbf{r} \\right] - \\sum_{\\sigma}\n",
+    "\\sum_{\\mathbf{q} \\mathbf{p} \\leq F} \\left[ \\int v(r) \\exp{-i (\\mathbf{q} \\cdot \\mathbf{r})} d\\mathbf{r} \\right] \\right).\n",
+    "$$"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "f3acd197",
+   "metadata": {},
+   "source": [
+    "The first term is the so-called direct term while the second term is the exchange term."
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "d1d59590",
+   "metadata": {},
+   "source": [
+    "## Potential energy\n",
+    "\n",
+    "We can rewrite this equation as (and this applies to any potential which depends only on the relative distance between particles)"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "edc51611",
+   "metadata": {},
+   "source": [
+    "<!-- Equation labels as ordinary links -->\n",
+    "<div id=\"eq:V_b\"></div>\n",
+    "\n",
+    "$$\n",
+    "\\begin{equation}\n",
+    "\\langle \\Phi_0\\vert \\hat{V} \\vert \\Phi_0\\rangle =\n",
+    "\\frac{1}{2V} \\left( N^2 \\left[ \\int v(r) d\\mathbf{r} \\right] - N \\sum_{\\mathbf{q}} \\left[ \\int v(r) \\exp{-i (\\mathbf{q}\\cdot \\mathbf{r})} d\\mathbf{r} \\right] \\right),\n",
+    "\\label{eq:V_b} \\tag{4}\n",
+    "\\end{equation}\n",
+    "$$"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "570a6c35",
+   "metadata": {},
+   "source": [
+    "where we have used the fact that a sum like $\\sum_{\\sigma}\\sum_{\\mathbf{k}}$ equals the number of particles. Using the fact that the density is given by\n",
+    "$\\rho = N/V$, with $V$ being our volume, we can rewrite the last equation as"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "658dc6af",
+   "metadata": {},
+   "source": [
+    "$$\n",
+    "\\langle \\Phi_0\\vert \\hat{V} \\vert \\Phi_0\\rangle =\n",
+    "\\frac{1}{2} \\left( \\rho N \\left[ \\int v(r) d\\mathbf{r} \\right] - \\rho\\sum_{\\mathbf{q}} \\left[ \\int v(r) \\exp{-i (\\mathbf{q}\\cdot \\mathbf{r})} d\\mathbf{r} \\right] \\right).\n",
+    "$$"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "a1835ddf",
+   "metadata": {},
+   "source": [
+    "## Interaction part\n",
+    "\n",
+    "For the electron gas\n",
+    "the interaction part of the Hamiltonian operator is given by"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "e7c1a9e7",
+   "metadata": {},
+   "source": [
+    "$$\n",
+    "\\hat{H}_I=\\hat{H}_{el}+\\hat{H}_{b}+\\hat{H}_{el-b},\n",
+    "$$"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "290ffbac",
+   "metadata": {},
+   "source": [
+    "with the electronic part"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "57aae2d4",
+   "metadata": {},
+   "source": [
+    "$$\n",
+    "\\hat{H}_{el}=\\sum_{i=1}^N\\frac{p_i^2}{2m}+\\frac{e^2}{2}\\sum_{i\\ne j}\\frac{e^{-\\mu |\\mathbf{r}_i-\\mathbf{r}_j|}}{|\\mathbf{r}_i-\\mathbf{r}_j|},\n",
+    "$$"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "77093303",
+   "metadata": {},
+   "source": [
+    "where we have introduced an explicit convergence factor\n",
+    "(the limit $\\mu\\rightarrow 0$ is performed after having calculated the various integrals)."
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "0836a32f",
+   "metadata": {},
+   "source": [
+    "## Positive background\n",
+    "\n",
+    "Correspondingly, we have"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "1b94911d",
+   "metadata": {},
+   "source": [
+    "$$\n",
+    "\\hat{H}_{b}=\\frac{e^2}{2}\\int\\int d\\mathbf{r}d\\mathbf{r}'\\frac{n(\\mathbf{r})n(\\mathbf{r}')e^{-\\mu |\\mathbf{r}-\\mathbf{r}'|}}{|\\mathbf{r}-\\mathbf{r}'|},\n",
+    "$$"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "54b88cb1",
+   "metadata": {},
+   "source": [
+    "which is the energy contribution from the positive background charge with density\n",
+    "$n(\\mathbf{r})=N/V$. Finally,"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "5ac1e158",
+   "metadata": {},
+   "source": [
+    "$$\n",
+    "\\hat{H}_{el-b}=-\\frac{e^2}{2}\\sum_{i=1}^N\\int d\\mathbf{r}\\frac{n(\\mathbf{r})e^{-\\mu |\\mathbf{r}-\\mathbf{x}_i|}}{|\\mathbf{r}-\\mathbf{x}_i|},\n",
+    "$$"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "4a66aba4",
+   "metadata": {},
+   "source": [
+    "is the interaction between the electrons and the positive background."
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "8622751c",
+   "metadata": {},
+   "source": [
+    "## Positive charge contribution\n",
+    "\n",
+    "We can show that"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "665c4596",
+   "metadata": {},
+   "source": [
+    "$$\n",
+    "\\hat{H}_{b}=\\frac{e^2}{2}\\frac{N^2}{V}\\frac{4\\pi}{\\mu^2},\n",
+    "$$"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "b436aa2b",
+   "metadata": {},
+   "source": [
+    "and"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "6a7bb83d",
+   "metadata": {},
+   "source": [
+    "$$\n",
+    "\\hat{H}_{el-b}=-e^2\\frac{N^2}{V}\\frac{4\\pi}{\\mu^2}.\n",
+    "$$"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "4492e3ef",
+   "metadata": {},
+   "source": [
+    "## Thermodynamic limit\n",
+    "\n",
+    "For the electron gas and a Coulomb interaction, these two terms are cancelled (in the thermodynamic limit) by the contribution from the direct term arising\n",
+    "from the repulsive electron-electron interaction. What remains then  when computing the reference energy is only the kinetic energy contribution and the contribution from the exchange term.  For other interactions, like nuclear forces with a short range part and no infinite range, we need to compute both the direct term and the exchange term. \n",
+    "\n",
+    "We can show that the final Hamiltonian can be written as"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "fef05044",
+   "metadata": {},
+   "source": [
+    "$$\n",
+    "H=H_{0}+H_{I},\n",
+    "$$"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "a9a220a8",
+   "metadata": {},
+   "source": [
+    "with"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "6a1469ba",
+   "metadata": {},
+   "source": [
+    "$$\n",
+    "H_{0}={\\displaystyle\\sum_{\\mathbf{k}\\sigma}}\n",
+    "\\frac{\\hbar^{2}k^{2}}{2m}a_{\\mathbf{k}\\sigma}^{\\dagger}\n",
+    "a_{\\mathbf{k}\\sigma},\n",
+    "$$"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "1b5249ab",
+   "metadata": {},
+   "source": [
+    "and"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "d0cf4bcc",
+   "metadata": {},
+   "source": [
+    "$$\n",
+    "H_{I}=\\frac{e^{2}}{2V}{\\displaystyle\\sum_{\\sigma_{1}\\sigma_{2}}}{\\displaystyle\\sum_{\\mathbf{q}\\neq 0,\\mathbf{k},\\mathbf{p}}}\\frac{4\\pi}{q^{2}}\n",
+    "a_{\\mathbf{k}+\\mathbf{q},\\sigma_{1}}^{\\dagger}\n",
+    "a_{\\mathbf{p}-\\mathbf{q},\\sigma_{2}}^{\\dagger}\n",
+    "a_{\\mathbf{p}\\sigma_{2}}a_{\\mathbf{k}\\sigma_{1}}.\n",
+    "$$"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "ca1effbb",
+   "metadata": {},
+   "source": [
+    "## Ground state energy\n",
+    "Calculate $E_0/N=\\langle \\Phi_{0}\\vert H\\vert \\Phi_{0}\\rangle/N$ for for this system to first order in the interaction. Show that, by using"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "c1bf4344",
+   "metadata": {},
+   "source": [
+    "$$\n",
+    "\\rho= \\frac{k_F^3}{3\\pi^2}=\\frac{3}{4\\pi r_0^3},\n",
+    "$$"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "77b36e0c",
+   "metadata": {},
+   "source": [
+    "with $\\rho=N/V$, $r_0$\n",
+    "being the radius of a sphere representing the volume an electron occupies \n",
+    "and the Bohr radius $a_0=\\hbar^2/e^2m$, \n",
+    "that the energy per electron can be written as"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "2cd16305",
+   "metadata": {},
+   "source": [
+    "$$\n",
+    "E_0/N=\\frac{e^2}{2a_0}\\left[\\frac{2.21}{r_s^2}-\\frac{0.916}{r_s}\\right].\n",
+    "$$"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "1e6974eb",
+   "metadata": {},
+   "source": [
+    "Here we have defined\n",
+    "$r_s=r_0/a_0$ to be a dimensionless quantity."
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "a6765f03",
+   "metadata": {},
+   "source": [
+    "## Exercise 2: plot of energy\n",
+    "\n",
+    "Plot your results. Why is this system stable?\n",
+    "Calculate thermodynamical quantities like the pressure, given by"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "5c726dbd",
+   "metadata": {},
+   "source": [
+    "$$\n",
+    "P=-\\left(\\frac{\\partial E}{\\partial V}\\right)_N,\n",
+    "$$"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "49b923e0",
+   "metadata": {},
+   "source": [
+    "and the bulk modulus"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "76f11238",
+   "metadata": {},
+   "source": [
+    "$$\n",
+    "B=-V\\left(\\frac{\\partial P}{\\partial V}\\right)_N,\n",
+    "$$"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "948e45b4",
+   "metadata": {},
+   "source": [
+    "and comment your results."
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "abe1a82b",
+   "metadata": {},
+   "source": [
+    "## Density functional theory\n",
+    "\n",
+    "Hohenberg and Kohn proved that the total energy of a system including\n",
+    "that of the many-body effects of electrons (exchange and correlation)\n",
+    "in the presence of static external potential (for example, the atomic\n",
+    "nuclei) is a unique functional of the charge density. The minimum\n",
+    "value of the total energy functional is the ground state energy of the\n",
+    "system. The electronic charge density which yields this minimum is\n",
+    "then the exact single particle ground state energy.\n",
+    "\n",
+    "In Hartree-Fock theory one works with large basis sets. This poses a\n",
+    "problem for large systems. An alternative to the HF methods is\n",
+    "DFT. DFT takes into account electron correlations but is less\n",
+    "demanding computationally than full scale diagonalization or Monte\n",
+    "Carlo methods."
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "1defce4c",
+   "metadata": {},
+   "source": [
+    "## Functional of density\n",
+    "\n",
+    "The electronic energy $E$ is said to be a functional of the\n",
+    "electronic density, $E[\\rho]$, in the sense that for a given function\n",
+    "$\\rho(r)$, there is a single corresponding energy. The\n",
+    "Hohenberg-Kohn theorem confirms that such a functional exists,\n",
+    "but does not tell us the form of the functional. As shown by Kohn and\n",
+    "Sham, the exact ground-state energy $E$ of an $N$-electron system can\n",
+    "be written as"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "fc7e27ee",
+   "metadata": {},
+   "source": [
+    "## More reading\n",
+    "1. R. van Leeuwen: Density functional approach to the many-body problem: key concepts and exact functionals, Adv. Quant. Chem. \\textbf{43}, 25 (2003). (Mathematical foundations of DFT)\n",
+    "\n",
+    "2. R. M. Dreizler and E. K. U. Gross: Density functional theory: An approach to the quantum many-body problem. (Introductory book)\n",
+    "\n",
+    "3. W. Koch and M. C. Holthausen: A chemist's guide to density functional theory. (Introductory book, less formal than Dreizler/Gross)\n",
+    "\n",
+    "4. E. H. Lieb: Density functionals for Coulomb systems, Int. J. Quant. Chem. \\textbf{24}, 243-277 (1983). (Mathematical analysis of DFT)"
+   ]
+  }
+ ],
+ "metadata": {
+  "kernelspec": {
+   "display_name": "Python 3 (ipykernel)",
+   "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": "3.9.15"
+  }
+ },
+ "nbformat": 4,
+ "nbformat_minor": 5
+}
diff --git a/doc/pub/week42/ipynb/ipynb-week42-src.tar.gz b/doc/pub/week42/ipynb/ipynb-week42-src.tar.gz
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diff --git a/doc/pub/week42/ipynb/week42.ipynb b/doc/pub/week42/ipynb/week42.ipynb
index e3e1eec8..a83517c7 100644
--- a/doc/pub/week42/ipynb/week42.ipynb
+++ b/doc/pub/week42/ipynb/week42.ipynb
@@ -2,7 +2,7 @@
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     "  * Start discussion of density functional theory\n",
     "\n",
     "  * Discussions of first midterm\n",
-    "<!-- * [Video of lecture TBA](https://youtu.be/) -->\n",
+    "\n",
+    "  * Video of lecture at <https://youtu.be/VbLlyZYRnYg>\n",
+    "\n",
+    "  * Whiteboard notes at <https://github.com/ManyBodyPhysics/FYS4480/blob/master/doc/HandwrittenNotes/2024/NotesOctober17.pdf>  \n",
     "\n",
     "2. Friday:\n",
     "\n",
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diff --git a/doc/src/week42/week42.do.txt b/doc/src/week42/week42.do.txt
index 7190cd72..54c8f621 100644
--- a/doc/src/week42/week42.do.txt
+++ b/doc/src/week42/week42.do.txt
@@ -11,7 +11,8 @@ o Thursday:
   * The first lecture is about the finalization of the calculation of the ground state energy of the homogeneous electron gas in three dimensions
   * Start discussion of density functional theory
   * Discussions of first midterm
-#    * "Video of lecture TBA":"https://youtu.be/"
+  * Video of lecture at URL:"https://youtu.be/VbLlyZYRnYg"
+  * Whiteboard notes at URL:"https://github.com/ManyBodyPhysics/FYS4480/blob/master/doc/HandwrittenNotes/2024/NotesOctober17.pdf"  
 o Friday:
   * Density functional theory
   * Discussions of  first midterm