Calculating Energy Levels in a 2-D Particle Box: Solving for n1 and n2

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SUMMARY

The discussion focuses on calculating the energy levels of a particle confined in a two-dimensional square box with dimensions L x L. The energy levels are determined using the formula E = (h²/8mL²)(n1² + n2²), where n1 and n2 are quantum numbers. Participants identified a total of eight unique combinations of (n1, n2) pairs that yield energy levels within the specified range of 0 to 16, correcting the initial count of five. Key combinations include (1,1), (1,2), (2,2), (1,3), (3,1), and (2,3).

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Homework Statement


For a particle in a square box of L*L dimension find how many energy levels are in the range of energy between 0 and 16 (h^2/8mL)



Homework Equations





The Attempt at a Solution


n1=1 n2 =1
n1=1 n2=2
n1=1 n2=2
n1=2 n2=2
n1=2 n2=3
i think there should be 8 total i am only getting 5
 
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myoplex11 said:
[
n1=1 n2 =1
n1=1 n2=2
n1=1 n2=2
n1=2 n2=2
n1=2 n2=3
i think there should be 8 total i am only getting 5

What about

n1=1 n2=3
n1=3 n2=1
n1=3 n2=2

Also, be careful with how you are defining your energy levels. I see that you have a duplicate, but I don't think that is what you really mean.
 

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