Does L'Hospital's rule apply to complex functions?

  • Thread starter quasar987
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  • #1
quasar987
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Main Question or Discussion Point

I have to evaluate

[tex]\lim_{x\rightarrow \infty} \frac{x-1}{e^{ipx/\hbar}}[/tex]

is this equal to

[tex]\lim_{x\rightarrow \infty} \frac{\hbar}{ip e^{ipx/\hbar}}[/tex]

??
 

Answers and Replies

  • #2
LeonhardEuler
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L'Hospital's rule only applies when a limit approaches [itex]\frac{0}{0}[/itex] or [itex]\frac{\infty}{\infty}[/itex]. Niether is the case here because [itex]\lim_{x\rightarrow\infty}e^{ix}[/itex] does not exist. The real and imaginary parts oscilate between -1 and 1 as x approaches infinity. Your limit is equal to:
[tex]\lim_{x\rightarrow \infty} \frac{x-1}{e^{ipx/\hbar}} =\lim_{x\rightarrow \infty} (x-1)\cos{\frac{ipx}{\hbar}}-i(x-1)\sin{\frac{ipx}{\hbar}[/tex]
So the real and imaginary parts both oscillate between larger and larger positive and negative numbers as x gets larger, so the limit does not exist.
 
  • #3
quasar987
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Dang. I guess I was trying a little too hard to make this QM problem work :tongue2:
 
  • #4
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ok so the answer is infinity
we have some thing bounded in the denominator
and the numerator goes to infinity
 
  • #5
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I suggest you choose different boundary conditions at infinity for your QM problem.
 

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