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Wave functions

  1. Mar 17, 2012 #1
    With the number i, its possible to create a wave function with just one variable.

    example:

    f(x)=i^x

    or..

    f(x)=2^ix

    But is there any wave function without the number i AND with only one(x and y) variable? can this be created?
     
    Last edited: Mar 17, 2012
  2. jcsd
  3. Mar 17, 2012 #2
    y = sin(x)
     
  4. Mar 17, 2012 #3
    Hello,

    Are you aware of the general equation of a wave?

    Hint: (It is a second order differential equation)
     
  5. Mar 18, 2012 #4

    chiro

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    Science Advisor

    If you want something that oscillates, then something of the form r(x)e^(ig(x)) will give you that. A standard linear wave will be in the form g(x) = wx + c corresponding to a shift and frequency information and if you want a 'real' waveform with the same peak and trough for every wavefront then r(x) = c.

    This expression will give you a complex wave-form with a real and imaginary component and if you want one or the other and not both you need to use the normal identities to get rid of the i term or the real term.
     
  6. Mar 18, 2012 #5

    HallsofIvy

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    Staff Emeritus
    Science Advisor

    In fact, it is possible to construct a one-dimensional wave of any shape.
     
  7. Mar 19, 2012 #6
    This is the same as

    y=1/2 i e^(-i x)-1/2 i e^(i x)

    so that would be "cheating"...
     
    Last edited: Mar 19, 2012
  8. Mar 19, 2012 #7
    does this mean i*g(x) (the imaginary unit times the function g of x)?
     
  9. Mar 19, 2012 #8
    I dont know anything about differential equations:(
     
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