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Commutative free particle time evolution

  1. Nov 26, 2012 #1
    1. The problem statement, all variables and given/known data

    http://img853.imageshack.us/img853/2532/70224197.png [Broken]

    2. Relevant equations

    i know schrödingher eq. and basic quantum formula

    3. The attempt at a solution

    i showed that the equality at the first question but i can not start from (a) part. how and where am i supposed to start for (a) part of question?
     
    Last edited by a moderator: May 6, 2017
  2. jcsd
  3. Nov 27, 2012 #2
    i even dont know what is the time evoluation of varience? what is that?
     
  4. Nov 27, 2012 #3

    vela

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    Forget quantum mechanics for a second. From basic statistics, if x is a random variable, its variance is ##\sigma^2 = E[(x-\bar{x})^2]##, where ##\bar{x}=E(x)##. Now how does this translate into quantum mechanics? It should be clear how the first part of the problem then applies to solving (a).
     
  5. Nov 27, 2012 #4
    thank you for your answer. now i am trying that

    [itex]\frac{dψ}{dt}[/itex] = [itex]\frac{iħ}{2m}[/itex] d2ψ/dx2

    after that i find that; (i send dt to right side)

    ψ = ∫ [itex]\frac{iħ}{2m}[/itex] d2ψ/dx2 dt

    but i dont know how can i take the integral of right side?

    after that i will use the <x> = ∫ψ* x ψ

    is that true?
     
  6. Nov 27, 2012 #5

    vela

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    I have no idea what you're doing.
     
  7. Nov 27, 2012 #6
    me too. im very confused. can you just tell me how can i find <x(t)> and <x(t)^2>
     
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