Contents

• List of Figures
• Ehrenfest's Theorem
  • Simple Harmonic Oscillator
  • Constant Force
• Conservation and Continuity
  • Solution of the TDSE
  • Verification of TDSE
  • Probability density
  • Net flow of probability
  • Probability Current
  • Prove that momentum is conserved in quantum mechanics
• The Energy Representation: Superposition Solutions to the TDSE
  • Time independence of the probability distribution for measuring energies
  • Conservation of Energy
  • Alternate Proof: Ehrenfest's Theorem
• Solutions of the Time Independent Schrödinger Equation (TISE)
  • Qualitative Solutions for Wave Functions
  • Lower energy solutions to the TDSE
  • Higher energy solutions to the TDSE
  • Reflection Time Delay
• About this document ...