Using software to solve eigenvalues of Hamiltonian

[4finger]

This is my first time posting in this forum, or any, so I'm sorry if something is out of place.

I'm doing undergrad research with a professor on quantum supercomputing and I need to use some software to find the eigenvalues of the energy using the Hamiltonian. He suggested I used maplesoft or this applet but I don't understand how these programs work.
http://fermi.la.asu.edu/schmidt/applets/seqn/plugschroedinger.html

My knowledge in this area doesn't extend very far. I've taken modern physics where I learned in general about quantum mechanics but not in depth. They mentioned that the Hamiltonian operator exists but never used it, I also saw it in classical mechanics. That's also where I learned about eigenfunctions while studying angular momentum. We solved it by taking the determinant but that only works for a discrete case and the Hamiltonian is continuous. I wouldn't know how to find the eigenvalues for a simple potential such as V=x or even V=5 let alone for this complicated one. I'm taking full quantum mechanics this term but that class only starts on 9/13.

The potential is roughly (x-y)^2/7.44 - cos(x), where x is the variable and y is the external flux. It comes from this article
http://www.physics.ucsb.edu/~martinisgroup/papers/Kofman2007.pdf
From what I understand, I have to find the value of the flux that will create a potential such that the left well will have 3 energy states and I need to find out exactly what those states are. It's not possible analytically so I have to use some kind of program for it. I'm still trying to figure it out using Maple and the applet. I can get a graph of the potential but I don't understand how the rest of the applet works.

Can someone please tell me how I can use Maple, or any other software for this. Or can you at least guide me in the right direction?

 

[mark726]

First of all, welcome to the forum! It's great to see someone interested in quantum supercomputing and taking on undergraduate research in this field. Don't worry about anything being out of place, we are all here to help and support each other in our scientific endeavors.

In terms of using Maple or other software for finding eigenvalues of the energy using the Hamiltonian, I would suggest reaching out to your professor or other colleagues who may have more experience with these programs. They can provide you with specific instructions and guidance on how to use the software for this particular problem.

In general, Maple is a computer algebra system that can perform mathematical computations and symbolic calculations. It has a wide range of functions and capabilities, including solving differential equations and finding eigenvalues. The applet you mentioned also seems to be a useful tool for solving the Schrodinger equation for a given potential.

Since you mentioned that you have taken modern physics and are currently taking full quantum mechanics, I would also suggest consulting with your professors or TAs for guidance on how to approach this problem. They can provide you with a better understanding of the Hamiltonian operator and how to use it to find eigenvalues for a given potential.

Finally, I would also recommend doing some background research on the potential you are working with, as well as on the methods and techniques used in quantum supercomputing. This will not only help you in understanding the problem better, but also in using Maple or other software more effectively.

Best of luck with your research and feel free to reach out to the forum for any further questions or concerns. We are all here to support each other's scientific pursuits.