What Is the Correct Normalization Constant for a Particle in a Cubic Box?

[jairusgarcia]

Homework Statement

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

Homework Equations

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

The Attempt at a Solution

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

 

[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.

 

[Gokul43201]

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?

 

[Gokul43201]

It should be A^2=L/8.

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

 

[Meir Achuz]

I think you may have inverted it.

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