updates

Author: msneubauer

_sources/lectures/LearningTheSchrodingerEquation.ipynb

@@ -1203,8 +1203,7 @@
         "id": "8d63241a"
       },
       "source": [
-        "In this notebook, we want to solve a Quantum Harmonic Oscillator consisting of a superposition of two states.\n",
-        "Note: We will use atomic units unless specified: $\\hbar=m=e=1$. \n",
+        "Next, we want to solve a Quantum Harmonic Oscillator consisting of a superposition of two states. Note: We will use atomic units unless specified: $\\hbar=m=e=1$. \n",
         "\n",
         "The governing equation is time-dependent Schrödinger equation\n",
         "\n",
@@ -1315,7 +1314,7 @@
       "source": [
         "We will restrict our domain to $\\mathbf{x} \\in [-\\pi,\\pi], t \\in [0,T]$, with fixed boundary conditions $x_0, x_b = 0$ in this notebook. \n",
         "\n",
-        "After you go through the notebook, feel free to play with the code for other domains. Let's create some data using the function you just wrote."
+        "After you go through the notebook, feel free to play with the code for other domains. Let's create some data using the function we just wrote."
       ]
     },
     {
@@ -1378,7 +1377,7 @@
       "id": "7668a65e",
       "metadata": {},
       "source": [
-        "Here `delta_T` and `delta_X` are the grid spacing in our domain. Data will be generated on this grid. You cna move the slider to see how the probabilty density of the QHO evolves in time. Our system looks like this:\n"
+        "Here `delta_T` and `delta_X` are the grid spacing in our domain. Data will be generated on this grid. The probabilty density of the QHO evolves in time and our system looks like this:"
       ]
     },
     {
@@ -2249,7 +2248,9 @@
         "id": "f15b1afe"
       },
       "source": [
-        "___<span style=\"color:Violet\">Exercise</span>___: What will the loss terms look like in this case? Hint: Split the Schrodinger equation in real and imaginary parts to calculate the equation loss.\n",
+        "___<span style=\"color:Violet\">Exercise</span>___: What will the loss terms look like in this case? \n",
+        "\n",
+        "Hint: Split the Schrodinger equation in real and imaginary parts to calculate the equation loss.\n",
         "\n",
         "Solution: The time-dependent Schrödinger equation can be written as\n",
         "\n",
@@ -2565,9 +2566,9 @@
         "\n",
         "Training time and accuracy both increase exponentially with collocation grid size.\n",
         "\n",
-        "<img src=\"https://raw.githubusercontent.com/GDS-Education-Community-of-Practice/DSECOP/main/Learning_the_Schrodinger_Equation/res/fig/pinn_colloc_time.png\" alt=\"Domain\" width=\"300\"/>\n",
+        "<img src=\"https://raw.githubusercontent.com/GDS-Education-Community-of-Practice/DSECOP/main/Learning_the_Schrodinger_Equation/res/fig/pinn_colloc_time.png\" alt=\"Domain\" width=\"400\"/>\n",
         "\n",
-        "<img src=\"https://raw.githubusercontent.com/GDS-Education-Community-of-Practice/DSECOP/main/Learning_the_Schrodinger_Equation/res/fig/pinn_colloc_performance.png\" alt=\"Domain\" width=\"300\"/>\n",
+        "<img src=\"https://raw.githubusercontent.com/GDS-Education-Community-of-Practice/DSECOP/main/Learning_the_Schrodinger_Equation/res/fig/pinn_colloc_performance.png\" alt=\"Domain\" width=\"400\"/>\n",
         "\n",
         "---\n"
       ]
@@ -2589,7 +2590,7 @@
       "source": [
         "We will now check the performance of NNs on systems with higher energy states. For demonstration, the system used is $\\psi_{1,3}(x,t)$.  The analytic solution is implemented in the method below (I will leave it to you to derive it)\n",
         "\n",
-        "let's write some code to compute it for arbitrary values of $x,t,\\omega$"
+        "Let's write some code to compute it for arbitrary values of $x,t,\\omega$"
       ]
     },
     {