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.