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The probability as an absolut value of the square of the amplitude

  1. Aug 17, 2010 #1
    All right, I don't have a problme with the concept, just a specific question.

    Is the absolute value of the amplitude abs(r^2 + (xi)^2) or abs(r^2) + abs((xi)^2)

    Or, to put it in a simpler way - Do you absolute the value of the square of the imaginary part?

    The difference would be, say

    2^2 + (5i)^2 = 4 + (-25) = (-21)
    abs(-21) = 21


    2^2 + (5i)^2 = 4 + (-25)
    abs(4) + abs(-25) = 29

    The latter seems more physically sound to me, but the former seems more mathemathically sound. Can anyone clear this up for me?
  2. jcsd
  3. Aug 18, 2010 #2
    The imaginary part is the part standing next to the "i", so in your example the 5 itself. Then you get the absolute value of the complex number by
    [tex]|z|^2 = \Re(z)^2+\Im(z)^2[/tex]
    Or by using the complex conjugate
    [tex]|z|^2 = z \cdot \bar z[/tex]

    For the first part I suspect you write your complex number in polar coordinates
    [tex] z = r \exp{i \xi}[/tex]
    In this case the absolute value would be just [tex]|z|=r[/tex]
  4. Aug 18, 2010 #3
    Ah, I think I see, the absolute value is the distance from the origin? Thanks for clearing it up.
  5. Aug 18, 2010 #4
    Yes. If you draw the complex number in the complex plane you can recognize the above formula as an application of Pythagoras' theorem.
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