Particle in a Box: Homework Statement & Equations

[chemasdf]

Homework Statement

hi

Homework Equations

The Attempt at a Solution

 

[The Bob]

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

 

[quantumdude]

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.

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

$$E_{m,n}=\frac{\hbar^2\pi^2}{2m}\left[\left(\frac{m}{L_x}\right)^2+\left(\frac{n}{L_y}\right)^2\right]$$

 

[chemasdf]

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

 

[quantumdude]

The ground state is $n=m=1$. I would take the first excited state to be the next highest energy level.

 

[chemasdf]

does this calculation involve any degenerate level considerations?

 

[quantumdude]

Why on Earth did you delete the problem statement?

 

[link2110]

maybe he found the answer? but then he should have deleted the post, not the question... weird...

 

[quantumdude]

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