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

1. Sep 26, 2005

### quasar987

I have to evaluate

$$\lim_{x\rightarrow \infty} \frac{x-1}{e^{ipx/\hbar}}$$

is this equal to

$$\lim_{x\rightarrow \infty} \frac{\hbar}{ip e^{ipx/\hbar}}$$

??

2. Sep 26, 2005

### LeonhardEuler

L'Hospital's rule only applies when a limit approaches $\frac{0}{0}$ or $\frac{\infty}{\infty}$. Niether is the case here because $\lim_{x\rightarrow\infty}e^{ix}$ does not exist. The real and imaginary parts oscilate between -1 and 1 as x approaches infinity. Your limit is equal to:
$$\lim_{x\rightarrow \infty} \frac{x-1}{e^{ipx/\hbar}} =\lim_{x\rightarrow \infty} (x-1)\cos{\frac{ipx}{\hbar}}-i(x-1)\sin{\frac{ipx}{\hbar}$$
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. Sep 26, 2005

### quasar987

Dang. I guess I was trying a little too hard to make this QM problem work :tongue2:

4. Jan 14, 2010

### nhrock3

ok so the answer is infinity
we have some thing bounded in the denominator
and the numerator goes to infinity

5. Jan 14, 2010

### Count Iblis

I suggest you choose different boundary conditions at infinity for your QM problem.