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Two level system Schrodinger Equation problem

  1. Oct 13, 2012 #1
    Hello guys,

    in the attached file, I can't understand how the guy arrived to the equation in the red rectangle.

    My problem is: how could there not be dC2/dt term. Why only dC1/dt term?
    ψ contains both C1 and C2, and when the derivative is applied, both have to be influenced, and both are functions of time. Why does C2 disappear?

    Could someone please explain how this last step is exactly taken?

    Thank you for any efforts.

    Attached Files:

    • 1.jpg
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  2. jcsd
  3. Oct 13, 2012 #2


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    Science Advisor

    Because it had been something like (dC1/dt) ψ1 + (dC2/dt) ψ2. But then he says "multiply by ψ1* and integrate over all space." Well, ∫ψ11 dx = 1 so you don't see it explicitly in the result, just dC1/dt is left in the first term. But ∫ψ12 dx = 0, by orthogonality, so the dC2/dt term drops out completely.
  4. Oct 14, 2012 #3
    Got it. Thanks man :)
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