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## Main Question or Discussion Point

What is the limit of [itex]e^{-ix}[/itex] as x tends to infinity?

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What is the limit of [itex]e^{-ix}[/itex] as x tends to infinity?

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Mark44

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What does ##e^{-ix}## represent? IOW, for a given x value, what does ##e^{-ix}## evaluate to?What is the limit of [itex]e^{-ix}[/itex] as x tends to infinity?

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[itex]cos(x) - isin(x)[/itex]

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Ray Vickson

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OK, so what do YOU think the limit should be, if anything?[itex]cos(x) - isin(x)[/itex]

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mathman

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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?

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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.

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Mark44

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What does ##e^{-ix}## represent? IOW, for a given x value, what does ##e^{-ix}## evaluate to?

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.[itex]cos(x) - isin(x)[/itex]

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