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Homework Help: Imaginary Normalisation Constant

  1. Jan 10, 2007 #1
    1. The problem statement, all variables and given/known data

    A one-dimensional system is in a state at time t=0 represented by:

    Q(x) = C { (1.6^0.5)Q1(x) - (2.4^0.5)Q2(x)}

    Where Qn(x) are normalised eergy eigenfunctions corresponding to different energy eigenvalues, En(n=1,2)

    Obtain the normalisation constant C


    3. The attempt at a solution

    I get C= i(1.2)^0.5 from the following equation:

    C^2 * (1.6 (int( Q1 ^2 dx) - 2.4(int ( Q2 ^2 dx = 1

    So C^2 has to be -5/4 in order for the above to be true. Is this right?
    Just a bit confused over whether it's possible to have an imaginary value for the normalisation constant? Thanks for any help you can give.
     
  2. jcsd
  3. Jan 10, 2007 #2
    You havent formed the product Q(x)Q*(x) correctly. What is special about energy eigenstates?
     
  4. Jan 10, 2007 #3
    they follow linear superposition? so the integral of the total wavefunction squared is equal to the integral of 1.6*Q1^2 plus the integral of 2.4*Q2^2?
     
  5. Jan 11, 2007 #4

    dextercioby

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    What is Q* equal to ? How do you define the scalar product?

    Daniel.
     
  6. Jan 11, 2007 #5
    Well there aren't any imaginary parts to the first wavefunction since its just in the form Q = C ( XQ1 - YQ2) so Q* is just the same as Q.
     
  7. Jan 11, 2007 #6

    Gokul43201

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    What do you know about the integral of Q1Q2*?

    Yes. Are you absolutely clear why this is so?
     
  8. Jan 11, 2007 #7
    I would think the integral of Q1Q2* would be zero since these wavefunctions are orthogonal, so I would end up with C^2 =5/20.
     
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