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Quantum - Find the formal expression of the coefficient cn(t=o)

  1. Oct 8, 2013 #1
    Quantum -- Find the formal expression of the coefficient cn(t=o)

    Hello everyone,
    I'm really stuck on the first question of an exercise, so I can't start!! :cry:
    1. The problem statement, all variables and given/known data
    ψ(x,t) a wave function normalized and solution of Shrodinger equation for a given potential.
    I the eigenfunctions are given by the ∅n(x) (supposed to be a phi) with eigen values En so we can write ψ(x,t) as:
    ψ(x,t)=Ʃ cn(t)∅n(x) = Ʃ cn(t=0)e^(-i*En*t/h)∅n(x)

    a. Find the formal expression of the coefficient cn(t=o) in terms of ∅n(x), and show the maths of your result by using the orthogonality of ∅n(x).

    2. Relevant equations



    3. The attempt at a solution
    Nothing, sadly.

    Thanks !!!!!
     
  2. jcsd
  3. Oct 9, 2013 #2

    ehild

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    You certainly learnt about the eigenfunctions of a Schrödinger equation???
    What does it mean that the eigenfunctions are normal?
     
  4. Oct 9, 2013 #3
    For eigenfunctions u(x) we have H*u(x)=E*u(x)
    Do you mean that the eigenfunctions are normalized ?
     
  5. Oct 9, 2013 #4

    ehild

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    Not only normalized, but also... ?

    Read the question:
    What does orthogonality mean? What is the inner product of two eigenfunctions?

    ehild
     
  6. Oct 12, 2013 #5
    Solved, it was really trivial.. !
    Thanks for your answers !
     
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