Analysis of Finite Square Potential Well: Bound and Scattering States

In summary, the person asking for help is reminded of the guidelines for using the HW help section of the forum and advised to seek the solution to their homework on their own. They are also reminded to ask specific questions rather than asking for a complete analysis and to utilize available resources such as textbooks and the internet.
  • #1
Hydeyuki
4
0
Hello, can anyone explain the full analysis of finite square potential well (bound state and scattering state) if

V(x) = -Vo, x <= 0 (region 1)
V(x) = 0, 0 < x < a (region 2)
V(x) = -Vo, x >= a (region 3)


It will be helpful if you can attach the analysis in .pdf format. Thank you in advance
 
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  • #2
I think you haven't read the guidelines for using the HW help section of the forum (useful read here https://www.physicsforums.com/showthread.php?t=94380). The idea is that you and I mean you should find the solution to your homework, not asking for someone else to solve your homework. And if possible, in greatest detail.

So no, nobody will explain to you the <full analysis of finite square potential well (bound state and scattering state) if

V(x) = -Vo, x <= 0 (region 1)
V(x) = 0, 0 < x < a (region 2)
V(x) = -Vo, x >= a (region 3)>

and most certainly nobody will attach a pdf with it.

You're invited to look for this analysis in your textbook, in other books, or on the internet and should you have any questions regarding the material you have found, post them here, but first try to find the answer by yourself before asking for help.
 

1. What is a finite square potential well?

A finite square potential well is a theoretical model used in quantum mechanics to describe the behavior of a particle in a confined region. It consists of a potential energy barrier on both sides and a finite potential energy well in between.

2. How does a particle behave in a finite square potential well?

In a finite square potential well, the particle's behavior is determined by its energy level and the height and width of the potential barriers. If the particle's energy is lower than the potential barrier, it will be confined within the well. However, if the particle's energy is higher than the potential barrier, it can escape the well.

3. What is the significance of a finite square potential well in quantum mechanics?

The finite square potential well is an important model in quantum mechanics as it allows us to study the behavior of particles in confined regions and understand phenomena such as tunneling and energy levels. It also has practical applications in fields such as material science and nanotechnology.

4. How is the Schrödinger equation used to solve for the energy levels in a finite square potential well?

The Schrödinger equation, a fundamental equation in quantum mechanics, is used to describe the behavior of particles in a potential energy field. To solve for the energy levels in a finite square potential well, we solve the Schrödinger equation for the particular potential energy function of the well. The solutions to the equation give us the allowed energy levels of the particle in the well.

5. What are some real-life examples of systems that can be described by a finite square potential well?

A finite square potential well can be used to model various physical systems, such as a particle trapped in a nanoscale box, a proton in a nucleus, and a quantum dot in a semiconductor. It can also be used to describe the behavior of electrons in a crystal lattice and the motion of atoms in a Bose-Einstein condensate.

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