How Does Resizing an Infinite Square Well Affect Ground State Probability?

In summary, the problem involves a particle in an infinite square well that is suddenly widened. The question is asking for the probability that the particle is in the ground state of the wider well, and the solution involves finding the overlap between the ground state of the smaller well and the ground state of the wider well. It is necessary to know the state of the particle in the smaller well, which is given as the ground state.
  • #1
cragar
2,552
3

Homework Statement


we have a particle in an infinite square well from x=0 to x=L/2
Then it says that we suddenly move the right hand side of the wall to x=L
and then it asks to find the probability that the particle is in the ground state of the widened well.

The Attempt at a Solution


Would I first find the wavefunction for the narrow well and then normalize it, and then normalize this again for the wider well.
 
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  • #2
Are you sure they didn't specify the state of the particle in smaller square well? Did they say it's in the ground state of the smaller well? You certainly need to know that before you can compute the overlap with the ground state in the larger square well.
 
  • #3
ya sorry they said it was in the ground state of the smaller well and they gave me the wave function for it.
 

FAQ: How Does Resizing an Infinite Square Well Affect Ground State Probability?

What is a square well potential?

A square well potential is a simplified model used in quantum mechanics to describe the behavior of a particle in a confined region. It consists of a potential energy function that is constant inside a certain region (the well) and infinite outside of it.

What is a square well wave function?

A square well wave function is the mathematical representation of the behavior of a particle in a square well potential. It describes the probability of finding the particle at a certain position within the well and how it evolves over time.

What are the properties of a square well wave function?

A square well wave function is continuous and smooth at all points within the well, and goes to zero at the boundaries of the well. It must also be normalized, meaning that the total probability of finding the particle within the well is equal to 1.

What is the significance of the energy eigenstates in a square well potential?

The energy eigenstates in a square well potential are the allowed energy levels that a particle can have within the well. These states determine the behavior and properties of the particle, such as its momentum and probability of being found at a certain position.

How does the depth and width of a square well potential affect the behavior of a particle?

The depth and width of a square well potential affect the energy eigenstates and the allowed energies of a particle within the well. A deeper well will have more energy levels and a wider well will result in lower energy levels. This ultimately affects the probability of finding the particle at certain positions within the well.

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