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E^ix formula

  1. Jan 11, 2012 #1
    On this page :
    http://www.ipod.org.uk/reality/reality_quantum_casino.asp [Broken]

    the guy present a function like this :

    ψ = A cos(x)

    then he says according to Euler formula, which is e^ix = cos(x) + i sin(x) :

    ψ = A e^ix ??

    shouldn't the result be instead :

    ψ + A*i*sin(x) = A cos(x) + A*i* sin(x)
    ψ + A*i*sin(x) = A (cos(x) + i sin(x))
    ψ = A e^ix - A*i*sin(x)
    ψ = A (e^ix - i sin(x))

    !!!
     
    Last edited by a moderator: May 5, 2017
  2. jcsd
  3. Jan 11, 2012 #2

    mathman

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    Gold Member

    ψ=Re(Aeix), where Re means real part.

    Your derivation of ψ has an error - last line should have -isin(x).
     
  4. Jan 11, 2012 #3
    ψ=A Re(eix) is a bit better since it doesn't assume that A was real.
     
  5. Jan 11, 2012 #4
    If you take only the real part, why "i" stays in the equation afterward ?
    How can a "Real" equation contains 'i' ?

    What I meant to say.. is that if you take Re-part it has to stay inside Re-parenthesis the whole calculation isn't it ?
     
    Last edited: Jan 11, 2012
  6. Jan 11, 2012 #5

    Ken G

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    Gold Member

    You can take a real part of any complex number, so it's fine to have "i" inside the "Re".
    I believe what is happening is that some people assume so automatically that we will be taking the real part at the end that they simply don't bother to write "Re[]" in every expression-- but it's there anyway.
     
  7. Jan 11, 2012 #6

    jtbell

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    Staff: Mentor

    This is just plain sloppy. It's what you get for using a random Web site instead of a real textbook. :yuck:
     
    Last edited by a moderator: May 5, 2017
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