Contents

• Representations (20 pts total)
  • Probabilities in the E representation (5 pts)
  • G representation (5 pts)
  • (*) Specification of the state from experimental information (5 pts)
  • Physical Prediction (5 pts)
• Operators (25 pts total)
  • Basic Properties of the operators R and L (5 pts)
  • Commutator (5 pts)
  • Rewriting the Hamiltonian (5 pts)
  • A very simple equation for the ground state (5 pts)
  • (*) First excited state (5 pts)
• Averages and Solutions of the TDSE (30 pts total)
  • Time evolution (7 pts)
  • (*) Center of the packet (8 pts)
  • General behavior of averages (7 pts)
  • Periodicity of averages in the SHO (8 pts)
• Solutions of the TISE (25 pts total)
  • Wavefunctions (8 pts)
  • Condition on Allowed Energy States (9 pts)
  • (*) Ground state energy independent of R (8 pts)
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