Calculate the energies of the six lowest states

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Homework Help Overview

The problem involves calculating the energies of the six lowest states for a particle confined in a two-dimensional box with specified dimensions. The subject area relates to quantum mechanics and the behavior of particles in potential wells.

Discussion Character

  • Exploratory, Conceptual clarification, Problem interpretation

Approaches and Questions Raised

  • The original poster attempts to derive energy equations but expresses uncertainty about the setup and correctness of their approach. Some participants question the need for multiple energy equations and suggest reviewing the derivation of the equations used.

Discussion Status

The discussion is ongoing with participants exploring the setup of the problem and clarifying the derivation of relevant equations. There is no explicit consensus, but guidance has been offered regarding the importance of understanding the derivation of the equations.

Contextual Notes

The original poster indicates a lack of clarity in setting up the problem and understanding the equations, which may affect their ability to proceed. There is an implication of needing to separate variables in the wavefunction for a two-dimensional case.

acusanelli
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Homework Statement



Suppose that a particle of mass m is confined to move in the x-y plane in a 2-dimensional box of length Lx = L and LY = ½ L. Calculate the energies of the six lowest states.


Homework Equations


not sure to set up this problem?


The Attempt at a Solution


the most I can get is
E = (h^2π^2(n1^2+.5n2^2))/ 2mL^2
E = (h^2π^2)/ mL^2
and I don't think this is right
 
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Why do you have two energy equations? You know how to separate the wavefunction and solve for it in 2 dimensions. What can you say about the total energy after you separated the variables?
 
thats because I don't know how to set the problem up, i pulled those equations out of the book and am not sure what I am doing
 
You should read how the first equation you listed was derived. That way you can reproduce it for your problem.
 

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