(adsbygoogle = window.adsbygoogle || []).push({}); Problem:

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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:

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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.

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# Eigen functions/values for many-body Hamiltonian with creation/annihilation operators

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