What Is Heisenberg Hamiltonian?

In summary, the conversation is about the Heisenberg Hamiltonian and its relation to magnetism in solid state matter. The Heisenberg Hamiltonian is the exchange energy between spins and is related to the renormalization group. The Heisenberg picture of operators is represented by O_H=e^{-iHt}O_Se^{iHt} and is used to describe the regular Hamiltonian in the reference frame of the Hamiltonian operator. It is also mentioned that magnetism is a property of solids.
  • #1
somy
137
0
Hi.
Can anyone tell me what exactly the "Heisenberg Hamiltonian" is?
I found it in an article related to: the renormalization group.
Thanks in advance.
Somy:smile:
 
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  • #2
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.
 
  • #3
The Heisenberg Hamiltonian I'm aware of is related to magnetism. It's the exchange energy between the spins
[tex] H=\sum_i \sum_{j \ne i} J_{ij} S_i \cdot S_j [/tex]
 
  • #4
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?
 
  • #5
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
[tex]O_H=e^{-iHt}O_Se^{iHt}[/tex]
[tex]O_H, O_S[/tex] are operators in Heisenberg and Schroedinger pictures.
 
  • #6
but I thout it was related to solid state of matter. the hamiltonian of the linking energies.
yes?
 
  • #7
Yes. That's what I posted, magnetism is a property of solids too.
 

1. What is the Heisenberg Hamiltonian?

The Heisenberg Hamiltonian is a mathematical operator used in quantum mechanics to describe the energy of a system made up of interacting particles. It takes into account the position, momentum, and spin of each particle in the system.

2. Who is Heisenberg and why is this Hamiltonian named after him?

Werner Heisenberg was a German physicist who developed the theory of quantum mechanics in the 1920s. He is known for his contributions to the uncertainty principle and for developing the Heisenberg Hamiltonian, which is named after him in recognition of his work.

3. How is the Heisenberg Hamiltonian used in physics?

The Heisenberg Hamiltonian is used in many areas of physics, particularly in quantum mechanics and condensed matter physics. It is used to calculate the energy of a system and to study the behavior of particles within the system, such as their spin and magnetic properties.

4. What are the key components of the Heisenberg Hamiltonian?

The Heisenberg Hamiltonian is made up of several mathematical terms, including the kinetic energy of particles, the potential energy due to the interactions between particles, and terms that describe the spin and magnetic properties of the particles in the system.

5. How does the Heisenberg Hamiltonian relate to the Schrödinger equation?

The Heisenberg Hamiltonian is used to solve the time-dependent Schrödinger equation, which describes the evolution of a quantum system over time. The Heisenberg Hamiltonian is used to calculate the energy of the system, which is a key component of the Schrödinger equation.

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