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Generalized Schrödinger equation

  1. Jan 20, 2014 #1
    This equation (see attachment) appears in one of Prof. Susskinds's lectures on Quantum Mechanics: in trying to differentiate the coefficients of the eigenvectors of a wave function with respect to time, an exponential e^(-iEt) is introduced for alpha.

    I can see that d/dt e^(-iEt) = -iE e^(-iEt), but why is the second part e^(-iEt) not in the top equation in the attachment? Is it disregarded because it's just a number?

    Thanks for any help provided!
     
  2. jcsd
  3. Jan 20, 2014 #2
    Attachment seems to have got lost.
     

    Attached Files:

    • QM.jpg
      QM.jpg
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  4. Jan 20, 2014 #3

    dextercioby

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    But the exponential is there, disguised under the form of 'alpha' in the rhs.
     
  5. Jan 20, 2014 #4
    OK, so [itex]\alpha[/itex]j(0)e-iEt has simply been conflated into [itex]\alpha[/itex]j? Can you just do that since e-iEt is not a constant?
    Thanks!
     
  6. Jan 20, 2014 #5

    dextercioby

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    The only variable is time. e^{-iEt} in units with hbar=1 gathers the time dependence of alpha.
     
  7. Jan 20, 2014 #6
    Aj is defined on the second line of your picture. It doesn't look like a constant to me.:smile:
     
  8. Jan 20, 2014 #7
    OK, thanks guys.
     
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