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Wave function

  1. Mar 31, 2010 #1
    A particle moving on a straight line is described by [tex]\psi(x)=\frac{1+ix}{1+ix^2}[/tex].
    Where is the particle likely to be found?
    I took the derivative of probability density with respect to x and equated it to 0. I got my answer to be x=0.643,-0.643,1.554i and -1.554i.
    Please tell me whether I am right or wrong or are there any other methods to solve this problem or not?
     
  2. jcsd
  3. Mar 31, 2010 #2

    dx

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    There is no reason for the expectation value to be at a stationary point of the probability density.

    You have to evaluate the integral <x> = ∫ψ*(x)xψ(x)dx = ∫xP(x)dx.
     
  4. Mar 31, 2010 #3
    But the question is about maximum probability of finding the particle, isn't it?
     
  5. Mar 31, 2010 #4

    dx

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    "Where is the particle likely to be found" usually means that they want you to find the expectation value of x.
     
  6. Mar 31, 2010 #5

    dx

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    Unless the exact wording of the question was "where is the particle most likely to be found". Then you would find the x which maximises P(x).
     
  7. Mar 31, 2010 #6
    So if the question is where the particle is most likely to be found, is my answer correct.
     
  8. Mar 31, 2010 #7

    dx

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    x is a real number, how did you get imaginary values?
     
  9. Mar 31, 2010 #8
    By factorising
     
  10. Mar 31, 2010 #9

    dx

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  11. Mar 31, 2010 #10
    Now I finally got it, thanks dx
     
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