Contents

• List of Figures
• The Energy Representation: Eigenstate Expansions
  • Orthogonality Condition
    • General Case
    • Specific Case
  • Parseval's Theorem
    • General Case
    • Specific Case
  • Energy operator
    • General Case
    • Specific Case
  • General Solutions of the Time Dependent Schrödinger Equation (TDSE)
    • General Case
    • Specific Case
  • Conservation of Energy
• Qualitative Solutions for Bound States
  • Sketches
  • Piecewise constant Potential
  • Eigenstates for the Simple Harmonic Oscillator (SHO)
  • Insights into special cases of analytic solutions
• Sudden Change in Potential
  • What happens
  • The probability of staying bound
  • Relevant time scale
  • Strengthening the potential
• ``Perturbations'' in Potential
  • Unperturbed states
  • Full solution
  • Effects of the perturbation
• About this document ...