# Calculating coherence time

1. Jan 19, 2014

### Observer Two

1. The problem statement, all variables and given/known data

I have the complex term $g(t) = e^{\frac{-|t|}{t_c}}$ which is the degree of the coherence.

2. Relevant equations

Now I want to verify that:

$t_c = \int_{-\infty}^\infty \! |g(t)|^2 \, dt$

3. The attempt at a solution

$\int_{-\infty}^\infty \! |g(t)|^2 \, dt = \int_{-\infty}^\infty \! |e^{\frac{-|t|}{t_c}}|^2 \, dt = \int_{-\infty}^\infty \! e^{\frac{-|t|}{t_c}} e^{\frac{|t|}{t_c}} \, dt = \int_{-\infty}^\infty \! 1 \, dt$

2 Problems now.

First: The integral doesn't have a value if I integrate from - infinity to infinity.
Second: The value of the indefinite integral is t. Not t_c.

What am I missing here?

2. Jan 19, 2014

### NasuSama

You didn't multiply $e^{-\frac{|t|}{t_c}}$ by itself. Instead, the second multiplier misses the negative sign. Check your work carefully and try again evaluating the integral.

3. Jan 19, 2014

### Observer Two

Huh? I'm really missing something here.

$|z|^2 = z z^*$

So if in my case $z = e^{\frac{-|t|}{t_c}}$ then

$z^* = e^{\frac{|t|}{t_c}}$

Or not?