Problem: ----------- I’m trying to understand how to generally find Eigen functions/values (either analytically or numerically) for Hamiltonian with creation/annihilation operators in many-body problems. Procedures: -------------- 1. I setup a simple case of finite-potential well with two in-distinguishable fermions (ignore spin for the moment). 2. I got the creation/annihilation field operators. 3. I second-quantized all the elements of the Hamiltonian (kinetic energy, well/external potential, and electron-electron electrostatic interaction). My question is how to proceed next? I have the Hamiltonian which is now function of the creation/annihilation operators. How can I solve for the many-body Eigen function/values after that? Thanks so much.