Why are Diagonal Elements of a Time-Dependent Perturbed Hamiltonian Often Zero?

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In summary, a perturbed TD-Hamiltonian is a Hamiltonian operator used in quantum mechanics to describe the time evolution of a system undergoing a perturbation or disturbance. It includes an additional term that accounts for the disturbance and can be used to model various external influences. It is used in calculations to solve the Schrödinger equation for a given system and has applications in the study of chemical reactions, particle behavior, and material properties. It is also utilized in the development of advanced technologies like quantum computers.
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Morten
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Why does a time-dependent perturbed Hamiltonian commonly have diagonal elements equal to zero?
 
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Because the perturbation is what is going to mix the eigenstates of the unperturbed Hamiltonian. But the diagonal elements could be non-zero: an actual physical perturbation could also shift the energy levels. Most often, it is easier to work with a perturbation that only mixes the states, so I would move the diagonal elements to the "unperturbed" Hamiltonian in such a case.
 
  • #3
Thanks!
 

1. What is a perturbed TD-Hamiltonian?

A perturbed TD-Hamiltonian is a type of Hamiltonian operator used in quantum mechanics to describe the time evolution of a system that is undergoing a perturbation or disturbance. It is an extension of the traditional time-dependent Hamiltonian, which accounts for the effects of an external influence on the system.

2. How is a perturbed TD-Hamiltonian different from a regular TD-Hamiltonian?

A perturbed TD-Hamiltonian includes an additional term that accounts for the perturbation or disturbance on the system. This term is often time-dependent, meaning it varies over time, and can be used to model a variety of external influences, such as electric or magnetic fields.

3. What types of systems can be described using a perturbed TD-Hamiltonian?

A perturbed TD-Hamiltonian can be used to describe any quantum system that is undergoing a perturbation or disturbance. This can include atoms, molecules, and other small particles, as well as larger systems such as crystals or solids.

4. How is a perturbed TD-Hamiltonian used in calculations?

In calculations, a perturbed TD-Hamiltonian is typically used to solve the Schrödinger equation for a given system. This equation describes the time evolution of a system and can be solved to determine the state of the system at any given time. The perturbed TD-Hamiltonian helps to account for the effects of a disturbance on the system's evolution.

5. What are some real-world applications of perturbed TD-Hamiltonians?

Perturbed TD-Hamiltonians have many practical applications, including in the study of chemical reactions, the behavior of particles in magnetic fields, and the properties of materials under external influences. They are also used in the development of quantum computers and other advanced technologies.

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