Calculate the energy levels for a generalized potential

[puneet203]

Hi,

I need to calculate the energy levels for a generalised potential, which forms a double well, on Matlab as part of a project but I need to understand it analytically first. There doesn't seem to be much information about the topic on the web or in books I checked.

I read the following paper: http://icpr.snu.ac.kr/resource/wop.pdf/J01/2003/042/R06/J012003042R060830.pdf , which I understand till the point where the energy-splitting term has been calculated. But terribly confused after that !

Can anyone please suggest on how to approach the problem and what texts might be helpful?

Cheers!

 

[eljose79]

Thank you for your question regarding calculating energy levels for a generalized potential with a double well using Matlab. I understand your frustration with the lack of information on this topic, but I am here to assist you in understanding the problem analytically and providing some suggestions for resources.

To begin, let's break down the problem into smaller steps. First, we need to understand what a generalized potential with a double well is. This type of potential is often used to describe the behavior of a system with two stable states, such as a particle in a double well potential or a quantum mechanical system with two energy levels. It is characterized by having two local minima and a barrier between them.

Next, we need to understand how to calculate the energy levels for this type of potential. This can be done using various methods such as perturbation theory, variational methods, or numerical methods. In your case, you have mentioned using the energy-splitting term, which is often calculated using perturbation theory. This involves expanding the potential around the minima and solving for the eigenvalues of the Hamiltonian.

Now, as for understanding the paper you have mentioned, it may be helpful to break down each step and try to understand it in smaller chunks. You can also try looking for other resources online, such as lecture notes or tutorials on perturbation theory or solving for energy levels in a double well potential. Additionally, some textbooks on quantum mechanics or mathematical physics may have a section on this topic that could be helpful.

In terms of approaching the problem on Matlab, I suggest breaking down the problem into smaller components and testing each step to ensure accuracy. You can also consult the Matlab documentation or forums for assistance with specific functions or code.

I hope this helps guide you in the right direction. Good luck with your project!

 

[Entropia]

Hi,

It's great that you are taking the time to understand the problem analytically before jumping into coding on Matlab. It shows a thorough and scientific approach. I understand that the topic of calculating energy levels for a double well potential may not be readily available in textbooks or online resources. My suggestion would be to reach out to a colleague or mentor who may have experience with this topic and can guide you in the right direction. Additionally, you can also try looking for research papers or articles on similar topics to gain a better understanding. Keep persevering and I am sure you will find the right resources to help you with your project. Best of luck!