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What is the limit of e^-ix

  1. Jan 27, 2015 #1
    What is the limit of [itex]e^{-ix}[/itex] as x tends to infinity?
     
  2. jcsd
  3. Jan 27, 2015 #2

    Mark44

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    What does ##e^{-ix}## represent? IOW, for a given x value, what does ##e^{-ix}## evaluate to?
     
  4. Jan 27, 2015 #3
    [itex]cos(x) - isin(x)[/itex]
     
  5. Jan 27, 2015 #4

    Ray Vickson

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    OK, so what do YOU think the limit should be, if anything?
     
  6. Jan 27, 2015 #5
    Well this is exactly my problem, I dont know. Perhaps I should have mentioned that I have considered the limit in terms of cos and sin and I'm not just asking you out of laziness. I would be inclined to say the limit does not exist. The reason I need to know is I am answering a question on square well potentials where solving schrodingers equation yields [itex]\psi(x)=Ae^{ikx} +Be^{-ikx}[/itex] outside of the well which in the region to the leftof the well simplifies to [itex]Ae^{ikx}[/itex] and I was wondering if this is because the wave function equals zero as x tends to minus infinity which implies B=0. I dont know if this is now the right place to ask this but if anyone can help that would be great.
     
  7. Jan 27, 2015 #6

    mathman

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    I can't comment on the physics question. However the original math question is answerable - there is no limit. You can envision it geometrically as being points on the unit circle in the complex plane. As x becomes infinite the point simply goes around the circle indefinitely.
     
  8. Jan 27, 2015 #7

    Ray Vickson

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    Do you know what it means when we say that a function, f(x), has a limit as x → ∞? Never mind the "epsilon-delta" stuff; just give an intuitive description.

    Alternatively, think of the graph y = cos(x). Do the y-values settle down to a fixed value as x becomes larger and larger?
     
  9. Jan 27, 2015 #8

    Matterwave

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    A (infinite) square well potential should not have waves outside of the well. Outside the well, the wave function should just be 0. A finite square well can have a non 0 wave function outside the well, but they should exponentially decay instead of oscillate (assuming a bound state). Recheck your answers.

    If you are dealing with scattering states, then the wave function must be a wave-packet, not a plane wave since plane waves are not normalizable.
     
  10. Jan 27, 2015 #9

    Mark44

    Staff: Mentor

    No, I was looking for a more specific answer, which @mathman gave you in post #6. In my question I specified "for a specific x value," so your response should have taken that into account.
     
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