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Expectation value of uncertainty

  1. Oct 15, 2011 #1
    1. The problem statement, all variables and given/known data
    Show that, if [H,A] = 0 and dA/dt = 0, then <&Delta;A> is constant in time.


    2. Relevant equations
    d<A>/dt = <i/ℏ[H,A] + dA/dt>


    3. The attempt at a solution
    I am trying to use the above equation to show that d<&Delta;A>/dt is 0, and I can get to d&Delta;A/dt = 0, but I can't figure out how to compute [H,&Delta;A]. The only thing I can think of is that since &Delta; A is just a function of A and A commutes with H, then &Delta; A also commutes with H, but I can't find a theorem that says that.
     
  2. jcsd
  3. Oct 16, 2011 #2

    dextercioby

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    What's the definition of [itex] \delta A [/itex] ? Then differentiate it wrt time and use Heisenberg's equation of motion.
     
  4. Oct 16, 2011 #3
    Sorry, I don't know Heisenberg's equation of motion. We haven't gone over it in class and it doesn't show up in my book until much later.
     
  5. Oct 17, 2011 #4

    dextercioby

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    What is the name of the equation you placed under <Relevant equations> ?
     
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