# Using software to solve eigenvalues of Hamiltonian

1. Sep 12, 2010

### 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?
1. The problem statement, all variables and given/known data

2. Relevant equations

3. The attempt at a solution