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Time Independent Schrodinger Equation

  1. Dec 2, 2015 #1
    1. The problem statement, all variables and given/known data Verify that a plane wave ψ(x) = Ae-ikx is a solution to the time independent Schrodinger equation for a free particle in one dimension. Can it be normalised? Why?


    2. Relevant equations


    3. The attempt at a solution
    My lecturer's notes are all over the place, which is frustrating. The only notes that I seem to have on this question, I cannot understand because they're scattered. If anyone has a link to a proof, or notes on it, I would be so grateful.
     
  2. jcsd
  3. Dec 2, 2015 #2

    Ken G

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    Gold Member

    Just look up the equation, and plug in that solution, and show it works. Then notice that the solution is infinite in space, with constant magnitude (it is a complex number of magnitude |A|2 but a phase that varies in space and time), so it cannot be normalized to unity when integrated over all space.
     
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