What are the variables in determining energy levels for a finite potential well?

In summary, a finite well is a potential well with a finite depth, resulting in a finite number of energy levels for particles to occupy. These energy levels are determined by solving the Schrödinger equation and have important implications in understanding particle behavior in potential wells. They are quantized and cannot be occupied at any arbitrary value. The energy levels greatly influence the behavior of particles within the well, including their probability of being found at a certain energy level, their motion, and their ability to escape.
  • #1
mju4t
2
0
Hi, I am trying to show that the energy levels for a finite potential well can be determined from these two equations[tex]\gamma[/tex] = kcot(-ka/2) for B=0 and [tex]\gamma[/tex] =-ktan(-ka/2) for A=0.

I think it has something to do with substituting in the value of k, but I'm not quite sure where to start...any help would be appreciated!

Thanks,
Alex
 
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  • #2
What's A? What's B? What's a? What's k? What are you talking about? Try and rephrase your question in the form of a question, please...

Also, post homework questions in the Homework Forums.
 

1. What is a finite well in terms of energy levels?

A finite well is a potential well with a finite depth, meaning that the potential energy is not infinite at any point. This results in a finite number of energy levels that particles can occupy within the well.

2. How are energy levels determined in a finite well?

The energy levels in a finite well are determined by solving the Schrödinger equation, which is a mathematical equation that describes the behavior of particles in quantum mechanics. The solution to this equation yields the allowed energy levels for particles in the finite well.

3. What is the significance of energy levels in a finite well?

The energy levels in a finite well have important implications in understanding the behavior of particles in potential wells. They determine the probability of finding a particle at a certain energy level, as well as the behavior of the particle when it encounters the walls of the well.

4. Can particles occupy any energy level in a finite well?

No, particles in a finite well can only occupy specific energy levels that are determined by the depth and shape of the potential well. These energy levels are quantized, meaning they can only take on certain discrete values, and cannot occupy any energy level in between.

5. How do energy levels in a finite well affect particle behavior?

The energy levels in a finite well greatly influence the behavior of particles in terms of their probability of being found at a certain energy level, their motion within the well, and their ability to escape the well. The energy levels also determine the spacing between energy levels, which can affect the behavior of the particles in the well.

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