Quantum particle in a 2 dimensional box

In summary, the conversation discussed a question about a physics assignment. The question was about why there are two solutions for task 4 a), one for odd n and one for even n. The person responding explained that it has to do with the parity of the wave functions and the symmetries around x=0. They also suggested a more symmetric way to write the wave function.
  • #1
Unskilled
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Homework Statement


I need some help :cry:

http://www.fysik.uu.se/kurser/1tt306/filer/TentKF06+short-answers.pdf [Broken]

On task 4 a) i don't understand why they have two solutions, one for odd n and the other for even n.
 
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  • #2
Unskilled said:

Homework Statement


I need some help :cry:

http://www.fysik.uu.se/kurser/1tt306/filer/TentKF06+short-answers.pdf [Broken]

On task 4 a) i don't understand why they have two solutions, one for odd n and the other for even n.

Hi there, I also study @ Uppsala ;) physics..

It has to do with the parity of the wave functions. Look on the symmetries around x=0. Ground state has zero nodes, 1st excited has one etc. Skiss the potetial and search for symmetry points.
 
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  • #3
Note there's no qualititative difference between the x and y directions. You could write the wavefunction more symmetrically as:

[tex] \psi_{nm} = C \sin \left( n \pi \frac{x-(-A)}{A-(-A)} \right) \sin \left( m\pi \frac{y-0}{B-0}\right) [/tex]

They just used some trig identities to rewrite this.
 
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1. What is a quantum particle in a 2 dimensional box?

A quantum particle in a 2 dimensional box is a theoretical model used in quantum mechanics to study the behavior of a particle confined to a two-dimensional space. This model assumes that the particle is free to move within the box but cannot escape its boundaries.

2. How is the energy of a quantum particle in a 2 dimensional box quantized?

The energy of a quantum particle in a 2 dimensional box is quantized because the particle's motion is restricted to specific energy levels, similar to a ladder where each rung represents a different energy level. This is due to the wave nature of the particle and the boundary conditions of the box.

3. What is the significance of the size of the box in a quantum particle in a 2 dimensional box?

The size of the box in a quantum particle in a 2 dimensional box has a significant impact on the energy levels and behavior of the particle. A smaller box results in higher energy levels and a higher probability of finding the particle at the edges of the box.

4. How does the uncertainty principle apply to a quantum particle in a 2 dimensional box?

The uncertainty principle states that it is impossible to know both the exact position and momentum of a particle simultaneously. In the case of a quantum particle in a 2 dimensional box, the more confined the particle is, the more uncertain its momentum becomes, and vice versa.

5. Can a quantum particle in a 2 dimensional box have negative energy?

No, a quantum particle in a 2 dimensional box cannot have negative energy. The lowest energy level, known as the ground state, is considered to be zero energy. Any additional energy levels must have a positive value, meaning they are above the ground state.

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