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

jairusgarcia
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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
 
Last edited:
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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.
 
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?
 
Meir Achuz said:
It should be A^2=L/8.
That doesn't look right. I think you may have inverted it...
 
Gokul43201 said:
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.
 
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