Contents

• List of Figures
• Derivation of Operators from the de Broglie Hypothesis (25 pts)
  • Completing the basic set from lecture
  • Powers of x and p
  • Arbitrary functions of x and p
  • Beyond one dimension
  • Hamiltonian operators
• Application of Operators (25 pts)
  • Normalization
  • Probability distributions
  • Expectations
  • Uncertainties
  • Pure states of energy
• Particle Trapped in a Cavity Revisited (25 pts)
  • Wave function
  • Momentum Distribution
  • Heisenberg Uncertainty Principle in Action
• Uncertainty Principle (25 pts)
  • Shift away the mean values
  • Generate an inequality
  • Separation of the terms
  • Two general uncertainty principles
  • Application to x and p
• About this document ...