Confusion with formulas for wavefunctions

[Cocoleia]

Homework Statement

I am working on this problem:

The formula I am given in my notes is:

I found a website which explains this problem, and they give this formula:

But then, their answer is:

And I don't see how they went from sqrt(8) to 2 on the numerator. I am confused which formula to use where.
I am confused as to which formula I should use... my notes don't make any difference between L1, L2 and L3, but then it doesn't matter in this case in the end.

 

[PeroK]

You have found a solution for the 3D problem. Yours is the 2D problem, which is slightly different.

 

[Cocoleia]

You have found a solution for the 3D problem. Yours is the 2D problem, which is slightly different.

The solution I found was supposed to be for the exact same problem I am working on. In this case do I use the formula from my notes ? Or there is a completely different one that I am forgetting ?

 

[Cocoleia]

You have found a solution for the 3D problem. Yours is the 2D problem, which is slightly different.

Could I use this one:

and then add the y-component somehow ?

 

[PeroK]

Could I use this one:
and then add the y-component somehow ?

You've found the 1D solution and the 3D solution. I think you are supposed to solve the 2D problem for yourself!

 

[eys_physics]

Could I use this one:
View attachment 115925
and then add the y-component somehow ?

Yes, your problem in 2- or 3 dimension is separable. That, is the wave function for the 2-dimensional problem can be written as a product of two wave functions, one depending on $x$ and the other on $y$.