# Heisenberg Hamiltonian

Hi.
Can anyone tell me what exactly the "Heisenberg Hamiltonian" is???
I found it in an article related to: the renormalization group.
Somy

## Answers and Replies

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dextercioby
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I haven't seen such thing either. Why don't you quote the paragraph from the article? The context should make sense, i suppose.

Daniel.

The Heisenberg Hamiltonian I'm aware of is related to magnetism. It's the exchange energy between the spins
$$H=\sum_i \sum_{j \ne i} J_{ij} S_i \cdot S_j$$

I could be wrong about this since it is venturing out of my area of knowledge, but isn't the Heisenberg Hamiltonian just the regular Hamiltonian in the reference frame of the Hamiltonian operator?

If I am wrong, what exactly the Heisenberg picture of operators?

elhinnaw said:
I could be wrong about this since it is venturing out of my area of knowledge, but isn't the Heisenberg Hamiltonian just the regular Hamiltonian in the reference frame of the Hamiltonian operator?
If I am wrong, what exactly the Heisenberg picture of operators?
Inha iscorrect, Heisenberg picture of operators means that
$$O_H=e^{-iHt}O_Se^{iHt}$$
$$O_H, O_S$$ are operators in Heisenberg and Schroedinger pictures.

but I thout it was related to solid state of matter. the hamiltonian of the linking energies.
yes???

Yes. That's what I posted, magnetism is a property of solids too.