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Why does a time-dependent perturbed Hamiltonian commonly have diagonal elements equal to zero?
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.
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.
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.
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.
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.