Register to reply

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

by ranytawfik
Tags: annihilation, creation, many-body, numerical
Share this thread:
Jun3-11, 04:17 PM
P: 11

Iím trying to understand how to generally find Eigen functions/values (either analytically or numerically) for Hamiltonian with creation/annihilation operators in many-body problems.


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.
Phys.Org News Partner Physics news on
UCI team is first to capture motion of single molecule in real time
And so they beat on, flagella against the cantilever
Tandem microwave destroys hazmat, disinfects
Jun3-11, 09:54 PM
Sci Advisor
P: 1,939

It would be easier to respond if you post some of your math that you've
already obtained in the first 3 steps.

If you're not familiar with Latex on this forum, try this thread:
Jun4-11, 08:28 AM
Sci Advisor
Bill_K's Avatar
P: 4,160
In general, the procedure is as follows:

1) Try to find the normal modes of your system, that is, transform your creation/annihilation operators to a basis in which the Hamiltonian is diagonal: H = ∑ ak*ak.

2) Find the states for each normal mode as a quantized harmonic oscillator. The ground state is |0k> such that ak|0k> = 0. The excited states are |nk> = (ak*)n|nk>.

If you can't do step (1), you'll have to use perturbation theory.

Jun4-11, 10:38 PM
P: 11
Eigen functions/values for many-body Hamiltonian with creation/annihilation operators

Thanks strangerep and Bill. I'll try to do what you suggested, Bill, and post a follow up with the detailed Latex equations and procedures.

Register to reply

Related Discussions
Why does this Bra Ket (with creation and annihilation operators) equal zero? Advanced Physics Homework 7
Fermion creation and annihilation operators Quantum Physics 2
Creation/annihilation operators Quantum Physics 16
Creation and Annihilation Operators in QM General Physics 3