Can Bethe Ansatz Solve Multiple Fermionic Particles in a 1D Infinite Well?

[xlines]

Hello!

I was wondering about Bethe Ansatz . From what I've read, BA applies to 1D systems of N fermionic particles.

Let's say I have solved 1D problem for one particle. Now, I want to setup some boundary conditions (e.g. infinite deep well) and insert, say 3 fermionic particles and extract exact wavefunction and energy of the ground state. Is this situation where Bethe Ansatz can help me out? If this is so, I would very much appreciate any help on the subject - if you can indicate how to apply BA to my problem or have any litterature that does NOT treat Heisenberg's model.

Thanks in advance!

 

[azntoon]

Yes, Bethe Ansatz can be used to solve for the exact wavefunction and energy of a multi-particle system in a 1D potential. However, it is not as straightforward as simply applying it to the single-particle solution you have already obtained. The Bethe Ansatz involves taking the multi-particle Hamiltonian and transforming it into an algebraic problem that can be solved analytically. This involves introducing a set of coupled equations known as the Bethe Ansatz equations which can then be solved to determine the eigenstates of the system. The literature on the Bethe Ansatz is quite extensive and there are many examples of how it can be applied to different 1D systems. If you would like to learn more about this topic, I suggest looking at some of the key papers on the subject, such as those by C.N. Yang and C. P. Yang.

 

[Entropia]

Hi there! Thank you for your question about Bethe Ansatz. Yes, BA can definitely be applied to your problem of multiple fermionic particles in a 1D system with boundary conditions. In fact, BA was originally developed for solving the Heisenberg model, but it has since been applied to many other systems as well.

To apply BA to your specific problem, you would need to first determine the Hamiltonian for your system, which would include the boundary conditions you mentioned. Then, using the BA method, you can find the exact wavefunction and energy of the ground state of your system.

There are many resources available on how to apply BA to different systems, so I would suggest doing some research and finding a specific paper or book that focuses on your exact problem. Some good resources to start with are "The Bethe Ansatz" by Vladimir E. Korepin, "The Bethe Ansatz: A Guide to the Literature" by Vadim B. Kuznetsov, and "Introduction to Bethe Ansatz" by Andreas Klümper.

I hope this helps and good luck with your research!