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Quantum Mechanics Superposition Question

  1. Feb 13, 2012 #1
    1. The problem statement, all variables and given/known data
    A particle in an infinite square well has as its initial wavefunction ψ(x,t=0) = (1/√2)[φ1 + φ3].

    Find |ψ(x,t)|2. Express it as a sinusoidal function of time using ω= π2*h/(2mL2).

    2. Relevant equations
    Note that φn = √(2/L)*sin(nπx/L) for a well of width L.

    3. The attempt at a solution

    I found something in my book which says that ψ(x,t) = Ʃbn*e-iωntφn.

    Therefore, my ψ(x,t) = (1/√2)[e-iω1t)φ1 + e-iω3t)φ3].

    Is that right so far?

    Then, I can compute |ψ(x,t)|2, but I don't see how that is going to give me an answer in terms of ω. I have ωn though.
     
  2. jcsd
  3. Feb 14, 2012 #2

    vela

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    How are ##\omega## and ##\omega_n## related to the energy of state n?
     
  4. Feb 16, 2012 #3
    When you say you found something in your book that says [itex]\Psi (x,t) = \sum_n b_n\ e^{-i\ \omega _n \ t}\ \psi _n(x)[/itex], do you know what that is?
    Also, do you know what [itex]\omega _n[/itex] actually is?
     
    Last edited: Feb 16, 2012
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