A little help with a two particle Hamiltonian

In summary, the speaker is working on a project and needs to understand how to calculate the spatial derivative of a two-particle Hamiltonian function G, which is dependent on the density matrix P, which is in turn dependent on R. The attached paper provides information on how to use the chain rule for this calculation.
  • #1
LeeT
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TL;DR Summary
A little help with a two-particle hamiltonian
Hello, I'm working on a project. I need to understand every equation in a paper.
I need to calculate the spatial derivative of G (d/dR), a two-particle Hamiltonian. However, G is a function of P- the density matrix and P is a function of R. Is it a "special derivative"?
Here is the attached paper. <Moderator's note: deleted for copyright reasons>
thank you very much,
Lee

Moderator's note: Paper can be found at:
https://doi.org/10.1063/1.3152120
 
Last edited by a moderator:
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  • #2
LeeT said:
the spatial derivative of G (d/dR), a two-particle Hamiltonian. However, G is a function of P- the density matrix and P is a function of R.
The derivative with respect to R of a function G which is a function of P, which is a function of R can be computed by the chain rule. Nothing ''special'' is needed.
 

FAQ: A little help with a two particle Hamiltonian

1. What is a two particle Hamiltonian?

A two particle Hamiltonian is a mathematical representation of the total energy of a system consisting of two particles. It takes into account the kinetic and potential energies of both particles and their interactions with each other.

2. How is a two particle Hamiltonian used in physics?

In physics, a two particle Hamiltonian is used to describe the behavior and dynamics of systems with two particles, such as atoms, molecules, and subatomic particles. It is a fundamental tool in quantum mechanics and is used to calculate properties of these systems, such as energy levels and transition probabilities.

3. What is the Schrödinger equation and how does it relate to a two particle Hamiltonian?

The Schrödinger equation is a fundamental equation in quantum mechanics that describes the time evolution of a quantum system. It is directly related to the two particle Hamiltonian, as the Hamiltonian operator is used in the equation to calculate the energy of the system at different points in time.

4. Can a two particle Hamiltonian be used for systems with more than two particles?

Yes, a two particle Hamiltonian can be extended to describe systems with more than two particles. However, the mathematical complexity increases significantly as the number of particles increases, making it more difficult to solve for the system's energy levels and properties.

5. What are some real-life applications of a two particle Hamiltonian?

A two particle Hamiltonian has many real-life applications, including in the fields of chemistry, material science, and particle physics. It is used to study the behavior of atoms and molecules, as well as the properties of materials and subatomic particles. It is also used in the development of technologies such as lasers and quantum computers.

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