Merge branch 'master' of https://github.com/QC-Edu/IntroQM

book/MultiDExercise1.md

@@ -3,10 +3,13 @@
 **Write the Time-Dependent Schrödinger equation for one particle, in three dimensions, confined by the time-dependent potential $V(x,y,z,t)$.**
 
 The time-dependent Schrödinger equation is:
+
 $$
 \hat{H} \Psi(x,y,z,t) = i \hbar \frac{d \Psi(x,y,z,t)}{dt}
 $$
+
 Substituting in the specific value of the Hamiltonian,
+
 $$
 \left(-\frac{\hbar^2}{2m}\frac{d^2}{dx^2}-\frac{\hbar^2}{2m}\frac{d^2}{dy^2}-\frac{\hbar^2}{2m}\frac{d^2}{dz^2} + V(x,y,z,t) \right) \Psi(x,y,z,t) = i \hbar \frac{d \Psi(x,y,z,t)}{dt}
 $$

book/ParticleIn1DBox.ipynb

@@ -175,7 +175,7 @@
     "1 &= \\left|A_n\\right|^2\\int_0^a \\sin^2\\left(\\tfrac{n \\pi x}{a}\\right) \\,dx \\\\\n",
     " &= \\left|A_n\\right|^2\\int_0^a \\tfrac{1}{2}\\left(1-\\cos \\left(\\tfrac{2n \\pi x}{a}\\right)\\right) \\,dx \\\\\n",
     " &=\\tfrac{\\left|A_n\\right|^2}{2} \\left( \\int_0^a 1 \\,dx - \\int_0^a \\cos \\left(\\tfrac{2n \\pi x}{a}\\right)\\,dx  \\right) \\\\\n",
-    " &=\\tfrac{\\left|A_n\\right|^2}{2} \\left( \\left[ x \\right]_0^a - \\left[\\frac{-a}{2 n \\pi}\\sin \\left(\\tfrac{2n \\pi x}{a}\\right) \\right]_0^a  \\right) \\\\\n",
+    " &=\\tfrac{\\left|A_n\\right|^2}{2} \\left( \\left[ x \\right]_0^a - \\left[\\frac{a}{2 n \\pi}\\sin \\left(\\tfrac{2n \\pi x}{a}\\right) \\right]_0^a  \\right) \\\\\n",
     " &=\\tfrac{\\left|A_n\\right|^2}{2} \\left( a - 0  \\right) \n",
     "\\end{align}\n",
     "$$\n",

book/SchrodingerEq.ipynb

@@ -164,7 +164,7 @@
    "source": [
     "#### 📝 Exercise: Show that the time-dependent Schrödinger equation for the complex conjugate of the wavefunction, $\\Psi^*$, is:\n",
     "$$ \n",
-    "-i \\hbar \\frac{d \\Psi^*(x,t)}{dt} = - \\frac{\\hbar}{2m} \\frac{d^2 \\Psi^*(x,t)}{dx^2} + V(x,t)\\Psi^*(x,t) \n",
+    "-i \\hbar \\frac{d \\Psi^*(x,t)}{dt} = - \\frac{\\hbar^2}{2m} \\frac{d^2 \\Psi^*(x,t)}{dx^2} + V(x,t)\\Psi^*(x,t) \n",
     "$$\n",
     "\n",
     "#### 📝 Exercise: What is the complex conjugate of \n",

book/_toc.yml

@@ -67,19 +67,19 @@ parts:
     - file: ParticleInMultiD.ipynb
       title: Particles confined in two and three dimensions
       sections:
-      - url: https://classroom.github.com/a/dOOP2PpB
+      - url: https://classroom.github.com/a/5LGPHyJD
         title: "Practice: Effective Low-Dimensional Systems"
-      - url: https://classroom.github.com/a/tR__Vztb
+      - url: https://classroom.github.com/a/BnZQkNi2
         title: "Practice: The Sudden Approximation in 2-D"
-      - url: https://classroom.github.com/a/jYuKLWfw
+      - url: https://classroom.github.com/a/TSS2Sbin
         title: "Practice: Interacting particles in a box"
-      - url: https://classroom.github.com/a/8wy0Ss-1
+      - url: https://classroom.github.com/a/gHbKRyrp
         title: "Quiz: MultiD P-in-Box"
 
     - file: Postulates.ipynb
       title: The Postulates of Quantum Mechanics
       sections:
-      - url: https://classroom.github.com/a/yN4Hktkg
+      - url: https://classroom.github.com/a/aby7w6cC
         title: "Quiz: Applying the Postulates"
 
     - file: OneElectronAtoms.ipynb