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Homework Help: Free particle <p>

  1. Jan 30, 2014 #1
    1. The problem statement, all variables and given/known data
    A free particle moving in one dimension is in the initial state ψ(x,0). Prove that
    <p> is constant in time by direct calculation (i.e., without recourse to the
    commutator theorem regarding constants of the motion).

    2. Relevant equations

    <p> = m*(d<x>/dt) ?
    ψ(x,0)= 1/(√(2∏))*∫Θ(k)e^(ikx)dk

    3. The attempt at a solution

    I am not really sure where to start... Should I find <x> ? is that the easiest way? And how do you this for a free particle ? stuff is confusing me. Can someone give me a start here...
  2. jcsd
  3. Jan 30, 2014 #2


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    Staff Emeritus
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    No, don't use this. Use the definition of the expectation value of an operator.

    What is the Hamiltonian for a free particle?
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