Particle in a box probability

1. Jan 21, 2007

jairusgarcia

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

A particle is in a cubic box with infinitely hard walls whose edges have length L. The wave functions of the particle are given by

$$\psi(x)=Asin\frac{n\pi(x)}{L}Asin\frac{n\pi(y)}{L}Asin\frac{n\pi(z)}{L}$$

a) Find the value of the normalization constant A.
b) Find the probability that the particle will be found in the range

2. Relevant equations

in a)--- both questions, do i really need to do the triple integral?

3. The attempt at a solution

is this right? $$A=L/8$$

Last edited: Jan 21, 2007
2. Jan 21, 2007

Meir Achuz

It should be A^2=L/8. You can use the fact that sin^2 averages to 1/2 to do the integral quickly.
For any given range, you would have to do the integral over those limits.

3. Jan 21, 2007

Gokul43201

Staff Emeritus
Yes, you need to do the triple integral - but it's essentially only doing the same integral thrice. Your value for A is incorrect. Also, typically, one doesn't write the wavefunction with the normalization constant A^3 as you've written above. Are you sure that's how it is in the question given to you?

4. Jan 21, 2007

Gokul43201

Staff Emeritus
That doesn't look right. I think you may have inverted it...

5. Jan 21, 2007

Meir Achuz

Sorry. It was all wrong. It should be A^2=8/L^3. I did it in my cubical head.