Energy eigenvalues and eigenstates (Lecture, 60 minutes)

spins_unit_schrodinger_time_evolution.ppt Pages 6-11

  • Start with the activity to get them working with simple time-dependent calculations
  • Discuss meaning of stationary states
  • Have students do short whiteboard activity for calculating the probability of finding a state at time t for a simple 2 level system
  • Emphasize what is special about starting in an eigenstate vs. a mixed state
  • Relate this to using a different operator: it will only remain a stationary state if that operator commutes with H
  • Introduce a name for the frequency of the oscillations between 2 states (in a 2 state system): Bohr frequency
  • By analog, discuss stationary states vs. oscillatory states in a continuous system - I used the square well from the PhET simulation to have students make meaning of what they were observing based on the 2 level system ideas: http://phet.colorado.edu/en/simulation/bound-states

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