Typos week 2

Author: Marius Hope

doc/pub/week2/ipynb/week2.ipynb

@@ -500,7 +500,7 @@
    "source": [
     "$$\n",
     "\\boldsymbol{P}_a=\\vert \\psi_a\\rangle \\langle \\psi_a\\vert = \\begin{bmatrix} \\vert \\alpha_0\\vert^2 &\\alpha_0\\alpha_1^* \\\\\n",
-    "                                                                   \\alpha_1\\alpha_0^* & \\vert \\alpha_1\\vert^* \\end{bmatrix},\n",
+    "                                                                   \\alpha_1\\alpha_0^* & \\vert \\alpha_1\\vert^2 \\end{bmatrix},\n",
     "$$"
    ]
   },
@@ -519,7 +519,7 @@
    "source": [
     "$$\n",
     "\\boldsymbol{P}_b=\\vert \\psi_b\\rangle \\langle \\psi_b\\vert = \\begin{bmatrix} \\vert \\beta_0\\vert^2 &\\beta_0\\beta_1^* \\\\\n",
-    "                                                                   \\beta_1\\beta_0^* & \\vert \\beta_1\\vert^* \\end{bmatrix}.\n",
+    "                                                                   \\beta_1\\beta_0^* & \\vert \\beta_1\\vert^2 \\end{bmatrix}.\n",
     "$$"
    ]
   },
@@ -558,8 +558,8 @@
    "source": [
     "$$\n",
     "\\boldsymbol{A}=\\lambda_a\\begin{bmatrix} \\vert \\alpha_0\\vert^2 &\\alpha_0\\alpha_1^* \\\\\n",
-    "                                                                   \\alpha_1\\alpha_0^* & \\vert \\alpha_1\\vert^* \\end{bmatrix} +\\lambda_b\\begin{bmatrix} \\vert \\beta_0\\vert^2 &\\beta_0\\beta_1^* \\\\\n",
-    "                                                                   \\beta_1\\beta_0^* & \\vert \\beta_1\\vert^* \\end{bmatrix}.\n",
+    "                                                                   \\alpha_1\\alpha_0^* & \\vert \\alpha_1\\vert^2 \\end{bmatrix} +\\lambda_b\\begin{bmatrix} \\vert \\beta_0\\vert^2 &\\beta_0\\beta_1^* \\\\\n",
+    "                                                                   \\beta_1\\beta_0^* & \\vert \\beta_1\\vert^2 \\end{bmatrix}.\n",
     "$$"
    ]
   },
@@ -742,7 +742,7 @@
    "metadata": {},
    "source": [
     "$$\n",
-    "\\sum_{i=0}^1\\boldsymbol{P}_i^{\\dagger}\\boldsymbol{P}_1=\\boldsymbol{I},\n",
+    "\\sum_{i=0}^1\\boldsymbol{P}_i^{\\dagger}\\boldsymbol{P}_i=\\boldsymbol{I},\n",
     "$$"
    ]
   },
@@ -1500,14 +1500,14 @@
    "source": [
     "## Simple  Hamiltonian models\n",
     "\n",
-    "In order to study get started with coding, we will study two simple Hamiltonian systems, one which we can use for a single qubit systems and one which has as basis functions a two-qubit system. These two simple Hamiltonians exhibit also something which is called level crossing, a feature which we will use in later studies of entanglement.\n",
+    "In order to get started with coding, we will study two simple Hamiltonian systems, one which we can use for a single qubit systems and one which has as basis functions a two-qubit system. These two simple Hamiltonians exhibit also something which is called level crossing, a feature which we will use in later studies of entanglement.\n",
     "\n",
     "We study first a simple two-level system. Thereafter we\n",
     "extend our model to a four-level system which can be\n",
     "interpreted as composed of two separate (not necesseraly identical)\n",
     "subsystems.\n",
     "\n",
-    "We let our hamiltonian depend linearly on a strength parameter $z$"
+    "We let our hamiltonian depend linearly on a strength parameter $\\lambda$"
    ]
   },
   {
@@ -1668,7 +1668,7 @@
     "is $\\vert 0 \\rangle$. At $\\lambda=1$ the $\\vert 0 \\rangle$ mixing of\n",
     "the lowest eigenvalue is $1\\%$ while for $\\lambda\\leq 2/3$ we have a\n",
     "$\\vert 0 \\rangle$ component of more than $90\\%$.  The character of the\n",
-    "eigenvectors has therefore been interchanged when passing $z=2/3$. The\n",
+    "eigenvectors has therefore been interchanged when passing $\\lambda=2/3$. The\n",
     "value of the parameter $X$ represents the strength of the coupling\n",
     "between the model space and the excluded space.  The following code\n",
     "computes and plots the eigenvalues."
@@ -1785,7 +1785,7 @@
    "metadata": {},
    "source": [
     "$$\n",
-    "\\vert 10\\rangle = \\vert 1\\rangle_{\\mathrm{A}}\\otimes \\vert 0\\rangle_{\\mathrm{B}}=\\begin{bmatrix} 0 & 1 & 0 &0\\end{bmatrix}^T,\n",
+    "\\vert 01\\rangle = \\vert 0\\rangle_{\\mathrm{A}}\\otimes \\vert 1\\rangle_{\\mathrm{B}}=\\begin{bmatrix} 0 & 1 & 0 &0\\end{bmatrix}^T,\n",
     "$$"
    ]
   },
@@ -1803,7 +1803,7 @@
    "metadata": {},
    "source": [
     "$$\n",
-    "\\vert 01\\rangle = \\vert 0\\rangle_{\\mathrm{A}}\\otimes \\vert 1\\rangle_{\\mathrm{B}}=\\begin{bmatrix} 0 & 0 & 1 &0\\end{bmatrix}^T,\n",
+    "\\vert 10\\rangle = \\vert 1\\rangle_{\\mathrm{A}}\\otimes \\vert 0\\rangle_{\\mathrm{B}}=\\begin{bmatrix} 0 & 0 & 1 &0\\end{bmatrix}^T,\n",
     "$$"
    ]
   },
@@ -1849,7 +1849,7 @@
    "metadata": {},
    "source": [
     "$$\n",
-    "H_0\\vert 10 \\rangle = \\epsilon_{10}\\vert 10 \\rangle,\n",
+    "H_0\\vert 01 \\rangle = \\epsilon_{01}\\vert 01 \\rangle,\n",
     "$$"
    ]
   },
@@ -1859,7 +1859,7 @@
    "metadata": {},
    "source": [
     "$$\n",
-    "H_0\\vert 01 \\rangle = \\epsilon_{01}\\vert 01 \\rangle,\n",
+    "H_0\\vert 10 \\rangle = \\epsilon_{10}\\vert 10 \\rangle,\n",
     "$$"
    ]
   },
@@ -1914,8 +1914,8 @@
    "source": [
     "$$\n",
     "\\boldsymbol{H}=\\begin{bmatrix} \\epsilon_{00}+H_z & 0 & 0 & H_x \\\\\n",
-    "                       0  & \\epsilon_{10}-H_z & H_x & 0 \\\\\n",
-    "\t\t       0 & H_x & \\epsilon_{01}-H_z & 0 \\\\\n",
+    "                       0  & \\epsilon_{01}-H_z & H_x & 0 \\\\\n",
+    "\t\t       0 & H_x & \\epsilon_{10}-H_z & 0 \\\\\n",
     "\t\t       H_x & 0 & 0 & \\epsilon_{11} +H_z \\end{bmatrix}.\n",
     "$$"
    ]
@@ -1936,7 +1936,7 @@
    "metadata": {},
    "source": [
     "$$\n",
-    "\\rho_0=\\left(\\alpha_{00}\\vert 00 \\rangle\\langle 00\\vert+\\alpha_{10}\\vert 10 \\rangle\\langle 10\\vert+\\alpha_{01}\\vert 01 \\rangle\\langle 01\\vert+\\alpha_{11}\\vert 11 \\rangle\\langle 11\\vert\\right),\n",
+    "\\rho_0=\\left(\\alpha_{00}\\vert 00 \\rangle\\langle 00\\vert+\\alpha_{01}\\vert 01 \\rangle\\langle 01\\vert+\\alpha_{10}\\vert 10 \\rangle\\langle 10\\vert+\\alpha_{11}\\vert 11 \\rangle\\langle 11\\vert\\right),\n",
     "$$"
    ]
   },