Heisenberg Hamiltonian for 2 Electron System: Get Relation (1)

Thread starter LagrangeEuler
Start date Feb 5, 2014
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Hamiltonian Heisenberg

In summary, the Heisenberg Hamiltonian is a quantum mechanical operator that describes the energy and dynamics of a system of particles. It takes into account the interactions between particles, including spin and position. It is a fundamental concept in quantum mechanics, derived from the Schrödinger equation. The Heisenberg Hamiltonian accounts for the spin and position of electrons through specific terms in its equation, and is crucial in understanding the behavior of 2 electron systems such as atoms and molecules.

Feb 5, 2014

LagrangeEuler

For two electron system ##\vec{S}_1##, ##\vec{S}_2##
[tex]\mathcal{H}=J\vec{S}_1\cdot \vec{S}_2=J(\frac{1}{2}(S_{tot})^2-\frac{3}{4}) (1)[/tex]
How you get relation (1)?

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Feb 5, 2014

M Quack

hint: [itex](\vec{S}_1+\vec{S}_2)^2[/itex]

Related to Heisenberg Hamiltonian for 2 Electron System: Get Relation (1)

1. What is the Heisenberg Hamiltonian for a 2 electron system?

The Heisenberg Hamiltonian is a quantum mechanical operator used to describe the energy of a system of particles. In the case of a 2 electron system, it takes into account the interactions between the two electrons, such as their spin and position.

2. What is the relation between the Heisenberg Hamiltonian and quantum mechanics?

The Heisenberg Hamiltonian is a fundamental concept in quantum mechanics, as it is used to describe the energy and dynamics of quantum systems. It is derived from the Schrödinger equation, which is the central equation of quantum mechanics.

3. How does the Heisenberg Hamiltonian account for the spin of electrons?

The Heisenberg Hamiltonian includes terms that describe the spin of electrons, such as the spin operators for each electron. These terms take into account the spin interactions between the two electrons in the system.

4. How does the Heisenberg Hamiltonian account for the position of electrons?

The Heisenberg Hamiltonian also includes terms that describe the position of the electrons, such as the position operators for each electron. These terms account for the positional interactions between the two electrons in the system.

5. What is the significance of the Heisenberg Hamiltonian in understanding the behavior of 2 electron systems?

The Heisenberg Hamiltonian is crucial in understanding the energy and dynamics of 2 electron systems, such as atoms and molecules. It allows scientists to make predictions about the behavior of these systems, and has been instrumental in the development of quantum mechanics and modern physics.