Finite square quantum well - depth

In summary, a finite square quantum well is a model used to study the behavior of particles in a confined region, such as a potential well with finite depth and width. The depth of the well is determined by the energy difference between the regions inside and outside of the well, and it affects the energy levels and behavior of particles within the well. A deeper well results in higher energy levels and a greater likelihood of confinement, while a shallower well allows for easier movement of particles. The depth of a finite square quantum well can be changed, but it is typically determined by the material properties.
  • #1
zheng89120
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Homework Statement



Find the condition on the depth of the finite square well such that one finds two even and one odd bound state energy eigenstates, but no other bound state solutions exist. Your answer should appear as a range of allowed well depths, say ? < Vdepth of well < ?

Homework Equations



Finite Square Quantum Well

The Attempt at a Solution



guess:

h2/8mL2 < Vdepth of well < 9h2/8mL2
 
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  • #2
Why don't you try solving for the energies of the bound states of a finite square well?
 

1. What is a finite square quantum well?

A finite square quantum well is a model used in quantum mechanics to describe the behavior of particles within a confined region, specifically a potential well with finite depth and width. It is often used to study the properties of electrons in semiconductor materials.

2. How is the depth of a finite square quantum well determined?

The depth of a finite square quantum well is determined by the difference in energy between the positively charged region outside the well and the negatively charged region inside the well. This energy difference creates a potential energy barrier that particles must overcome to enter or leave the well.

3. What is the significance of the depth of a finite square quantum well?

The depth of a finite square quantum well affects the energy levels and behavior of particles within the well. A deeper well results in higher energy levels and a greater likelihood of particles being confined within the well, while a shallower well allows for easier passage of particles in and out of the well.

4. How does the depth of a finite square quantum well impact particle behavior?

The depth of a finite square quantum well determines the probability of finding particles within the well at a given energy level. A deeper well leads to a larger number of energy levels and a greater probability of finding particles at higher energy levels, while a shallower well results in fewer energy levels and a lower probability of finding particles at higher energy levels.

5. Can the depth of a finite square quantum well be changed?

Yes, the depth of a finite square quantum well can be changed by altering the potential energy barrier between the regions inside and outside the well. This can be done by applying an external electric field or by changing the composition of the well material. However, the depth is typically determined by the properties of the material and cannot be easily changed in practical applications.

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