Particle in a Box: Homework Statement & Equations

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Discussion Overview

The discussion revolves around a homework problem related to the quantum mechanics concept of a particle in a box, specifically focusing on the equations and quantum numbers involved in a two-dimensional scenario. Participants explore the implications of the equations and seek clarification on the quantum numbers.

Discussion Character

  • Homework-related
  • Technical explanation
  • Debate/contested

Main Points Raised

  • One participant questions the interpretation of L^2 as an area and suggests it may be manipulable.
  • Another participant points out that the energy equation provided is for a 1D particle in a box and notes that a 2D problem requires two quantum numbers.
  • Wavefunctions and energy equations for a 2D box are shared, indicating the need for both m and n quantum numbers.
  • A participant expresses difficulty in determining the quantum numbers and requests hints for solving for "n".
  • It is mentioned that the ground state is n=m=1, with the first excited state being the next highest energy level.
  • One participant raises a question about whether the calculation involves degenerate level considerations.
  • There is a discussion about the deletion of the original problem statement, with participants expressing concern over the impact on the thread's usefulness.

Areas of Agreement / Disagreement

Participants express varying levels of understanding and concern regarding the quantum numbers and the implications of the equations. There is no consensus on how to approach the problem or the appropriateness of deleting the original question.

Contextual Notes

There are unresolved aspects regarding the assumptions needed to determine the quantum numbers, as well as the implications of the equations for different dimensional scenarios. The deletion of the problem statement may limit the context for responses.

chemasdf
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Homework Statement



hi

Homework Equations





The Attempt at a Solution

 
Last edited:
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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
 
chemasdf said:

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
 
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?
 
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...
 
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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