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jimmycricket
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What is the limit of [itex]e^{-ix}[/itex] as x tends to infinity?
What does ##e^{-ix}## represent? IOW, for a given x value, what does ##e^{-ix}## evaluate to?jimmycricket said:What is the limit of [itex]e^{-ix}[/itex] as x tends to infinity?
jimmycricket said:[itex]cos(x) - isin(x)[/itex]
jimmycricket said:Well this is exactly my problem, I don't 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 don't know if this is now the right place to ask this but if anyone can help that would be great.
jimmycricket said:Well this is exactly my problem, I don't 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 don't know if this is now the right place to ask this but if anyone can help that would be great.
Mark44 said: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.jimmycricket said:[itex]cos(x) - isin(x)[/itex]
The limit of e^-ix as x approaches infinity is equal to 0.
The limit of e^-ix as x approaches 0 is equal to 1.
The limit of e^-ix as x approaches a complex number is equal to e^-ix.
The limit of e^-ix as x approaches negative infinity is equal to infinity.
The derivative of e^-ix is equal to -ie^-ix.