# Probability to Find a Particle

1. Apr 18, 2014

### Nugso

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

Suppose we have a particle in 1-dimension, with wavefunction $$Ae^{-\frac{|x|}{2d}}$$ . What is the probability to find the particle in the interval [0,d]?
Please provide your answer in terms of A, d, mathematical constants such as π (entered as pi) or e (entered as e). (Assume that A is real)

2. Relevant equations

$$∫ψ²dx = 1$$

3. The attempt at a solution

I think I need to find A by normalizing it. $$∫ψ²dx = 1$$

By integrating it, I get $$A= 1/\sqrt{2d}$$

Now, I have to integrate it again, but this time with the interval of [0,d]

$$∫1/sqrt(2d)*e^{-\frac{|x|}{2d}}*1/sqrt(2d)*e^{-\frac{|x|}{2d}}dx$$

and the answer I'm finding is, $$1/2*(1-e^{-1/d})*d$$

But somehow the answer is wrong. How do I correct it?

Last edited: Apr 18, 2014
2. Apr 18, 2014

### BOYLANATOR

I would check your solution for A again.

3. Apr 18, 2014

### Dick

Check it again. How did you wind up with a -1/d in the exponent?

4. Apr 23, 2014

### Nugso

Sorry for the late reply. I checked it and corrected the mistake.