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Homework Help: Quantum Mechanics - Superposition of Wavefunctions?

  1. Jan 26, 2012 #1
    1. The problem statement, all variables and given/known data
    The wavefunction for a particle in one dimension is given by
    ψ1. Another state the particle may be in is ψ2. A third state the particle could be in is ψ3.

    Looking at the wavefunctions, ψ3 is ψ1 and ψ2 added together.

    Is the probability of being in a given interval in ψ3 the same as the separate probabilities for ψ1 and ψ2 for that interval?

    2. Relevant equations



    3. The attempt at a solution
    I don't really understand how superposition works. I read something about the ψ's being linear, so a linear combination of ψ1 and ψ2 (ie. ψ3) is still a solution to the Schrodinger equation.

    Is the superposition state a completely different state still though? I don't get why I am being asked this question. If it's a mixture of the two states, the probabilities would change wouldn't they? I don't see the link here.
     
  2. jcsd
  3. Jan 26, 2012 #2

    vela

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    Suppose the particle is in the state ψ1 and say the probability of finding it in the interval a ≤ x ≤ b is p1. Similarly, suppose the particle is in the state ψ2 and the corresponding probability is p2, and likewise for state ψ3.

    The question is asking you, I believe, if it's true that p3 = p1 + p2.
     
  4. Jan 26, 2012 #3
    Thanks! I believe you're right.

    In general, I don't think p3 = p1 + P2.

    I don't think I could explain why though. I just don't see WHY those would be equal, because although state 3 is a superposition, it is still a new state is it not? Is there some situation in which p3 = p1 + P2 is true?
     
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