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

In summary, there are a total of 8 energy levels for a particle in a square box with dimensions of L*L and an energy range of 0 to 16 (h^2/8mL). This is determined by the combinations of n1 and n2 values, where n1 and n2 represent the quantum numbers for the energy levels. However, there was a mistake in the original calculation as it only accounted for 5 energy levels instead of 8. Additionally, the energy levels n1=1 and n2=2 were duplicated, making the total number of distinct energy levels 7 instead of 8. Further consideration should also be given to additional combinations such as n1=1 n2=3, n
  • #1
myoplex11
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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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  • #2
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.
 

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

1. What is a "Particle in a 2-D box"?

A "Particle in a 2-D box" refers to a simple model used in quantum mechanics to understand the behavior of a particle confined to a two-dimensional space. It involves a particle moving freely within a confined area, such as a box.

2. How is the energy of a "Particle in a 2-D box" quantized?

The energy of a "Particle in a 2-D box" is quantized because the particle is confined to a small space and can only have certain discrete energy levels. These energy levels are determined by the dimensions of the box and the mass of the particle.

3. What is the significance of the boundary conditions in a "Particle in a 2-D box"?

The boundary conditions in a "Particle in a 2-D box" are important because they determine the allowed energy levels and wave functions of the particle. These conditions are set by the dimensions of the box and affect the behavior of the particle within it.

4. How does the behavior of a "Particle in a 2-D box" differ from that of a particle in free space?

A "Particle in a 2-D box" is confined to a specific area, whereas a particle in free space can move freely in all directions. This confinement leads to quantization of energy levels and changes in the particle's behavior, such as the formation of standing waves.

5. What real-life applications does the concept of "Particle in a 2-D box" have?

The concept of "Particle in a 2-D box" is used in various fields, such as materials science and nanotechnology, to understand the behavior of particles in confined spaces. It also has applications in quantum computing and the development of new electronic devices.

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