Particle in a box

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

hi

2. Relevant equations



3. The attempt at a solution
 
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Hey Chemasdf,

Welcome to PF!

In respect to your question, L^2: an area maybe? I hope someone will correct me if I'm wrong that this can be manipulated.

The Bob
 

Tom Mattson

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3. The attempt at a solution
I have tried relating it to Energy in the equation E=(n^2*h^2)/(8mL^2). It is a 2D problem for particle in a box
You're using the formula for the 1D particle in a box. If you're talking about a 2D box then there should be 2 quantum numbers, not just one.

Wavefunctions and energies for the 2D box are given below.

[tex]\psi_{m,n}(x,y)=\frac{2}{\sqrt{L_xL_y}}\sin\left(\frac{m\pi x}{L_x}\right)\sin\left(\frac{n\pi y}{L_y}\right)[/tex]

[tex]E_{m,n}=\frac{\hbar^2\pi^2}{2m}\left[\left(\frac{m}{L_x}\right)^2+\left(\frac{n}{L_y}\right)^2\right][/tex]
 
I'm still having trouble determining the quantum numbers (n). Can someone give me a hint as to how to solve for "n". I cannot find the wavenumber without knowing the "n" which is not given. Thanks
 

Tom Mattson

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The ground state is [itex]n=m=1[/itex]. I would take the first excited state to be the next highest energy level.
 
does this calculation involve any degenerate level considerations?
 

Tom Mattson

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Why on Earth did you delete the problem statement?
 
maybe he found the answer? but then he should have deleted the post, not the question...o_O weird...
 

Tom Mattson

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Even if he did find the answer, people took the time to reply. It's disrespectful to destroy a thread like this.
 

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