Chapter 2 - Time-Independent Schrödinger Equation

Wave Equations

  • Differential operators
  • Two non-relativistic limits of the Dirac equation
  • Free particles
  • Expectation value equations
  • Separation of variables

    • Particle in a Box

  • Constant potential, named series
  • Expansion solution
  • (continued)
  • Infinite square well
  • Boundary conditions
  • Normalization
  • Solutions
  • Finite square well
  • Solutions

    • Barrier penetration

  • Barrier penetration
  • Tunnelling
  • Simultaneous solution
  • Reflections and transmission
  • Transmission

    Applications

  • Examples of tunnelling
  • KE and PE for alpha decay
  • Transparency of rectangular barrier
  • Tries per second
  • Four chains
  • Variable barrier thickness
  • Radioactive decay
  • Ammonia maser
  • STM animation
  • Atomic corral
  • Muon-catalyzed fusion

    • Harmonic Oscillator

  • Natural units; radial diff. equ.
  • Ansatz for 2-term recursion
  • Recursion relation
  • Termination condition
  • Wave function plots
  • Probability plots
  • Plot n=10
  • Hermite polynomials
  • French mathematicians