I really need a resource to explain the linear potential well to me

In summary, the speaker is struggling to understand a concept that involves making a substitution to solve a differential equation, which leads to finding energy eigenvalues based on the roots of the Airy equation. They are frustrated with resources that skip steps and are looking for a comprehensive explanation, possibly in the form of a video. They also express confusion about the topic and ask for more specific clarification.
  • #1
richyw
180
0
So I am trying to learn this. It is not making sense to me. Every single resource I have found tells me I need to make some weird substitution, and then it becomes a differential equation that has the Airy equation as a solution, and then skips to finding the energy eigenvalues as a function of the roots of the Airy equation.

Everything is skipping steps and I honestly can't see what is going on. Does anyone know of a video that explains this? Or a resource that shows EVERY step. I'm pulling my hair out over this one. My textbook kindly gave me a picture of the solutions, with not mention at all on how to solve it. Youtube seems to be devoid of videos. It seems crazy to me that no one has made a video on like the first potential we ever learn about in physics...
 
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  • #2
How can you expect us to help when you don't actually tell us what you're asking about? What exactly is it that's confusing you?
 

1. What is a linear potential well?

A linear potential well is a theoretical model used in quantum mechanics to describe the potential energy of a particle confined to a one-dimensional space. It is represented by a V-shape graph, with the bottom of the "V" representing the lowest energy state and the sides representing the walls of the well.

2. How does a linear potential well work?

In a linear potential well, the particle is free to move within the boundaries of the well, but is confined from moving outside of it. The particle can have different energy levels, with the lowest energy level being the ground state. The potential energy increases as the particle moves away from the center of the well.

3. What is the significance of the linear potential well in quantum mechanics?

The linear potential well is an important model in quantum mechanics because it helps us understand the behavior of particles in confined spaces. It is used to explain phenomena such as the energy levels of electrons in atoms and the behavior of particles in a semiconductor material.

4. What factors affect the behavior of a particle in a linear potential well?

The behavior of a particle in a linear potential well is affected by the depth and width of the well, as well as the mass and charge of the particle. The deeper and narrower the well, the more confined the particle is, and the smaller its energy levels will be. The mass and charge of the particle also affect its energy levels and the shape of the potential well.

5. Can you provide an example of a real-life application of the linear potential well?

One example of a real-life application of the linear potential well is in the design of semiconductor devices, such as transistors. The energy levels of electrons in a semiconductor material are determined by the potential well, and controlling these energy levels allows us to manipulate the flow of current in electronic circuits.

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