Ehrenfest's Theorem

Background: This problem shows how Ehrenfest's Theorem may be used to make precise statements about the behavior of quantum expectations, giving results equivalent to those expected from solving the full Time Dependent Schrodinger's Equation, which generally requires much more work. This problem also illustrates the fact that our theory satisifies the demands put on it by the JJ Thomson experiments which measured , namely that the motion of the centers of quantum wavepackets follow trajectories which may be described using the familiar equations from 8.01.

In this problem, you will consider a particle subjected to a constant force , so that its Hamiltonian is given by

Assignment:

• Apply Ehrenfest's Theorem
  • Generate the equations
  • Solve the equations
  • Interpret your results
• Full Solution
  • Generate the equations
  • Solve the equations
  • Interpret your results