Interaction picture

Interaction picture is a description of the dynamics in quantum mechanics where the potential V^ (x, t) is taken into account. In this picture, the wave functions and operators are time-dependent due to the presence of the potential. However, in the absence of the potential, the interaction picture reduces to the Heisenberg picture where the operators are time-dependent but the wave functions remain stationary.From: Introduction to Quantum Control and Dynamics [2019], Solid State and Quantum Theory for Optoelectronics [2019]

An Introductory Review of Quantum Mechanics

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Published in Ramaswamy Jagannathan, Sameen Ahmed Khan, Quantum Mechanics of Charged Particle Beam Optics, 2019

Ramaswamy Jagannathan, Sameen Ahmed Khan

The interaction picture is designed for use in time-dependent perturbation theory, where the goal is to study the time evolution of a system with a small time-dependent perturbation Hamiltonian. The time-evolution equation for |Ψi (t)〉, (3.462), can be formally integrated to give

Locally acting mirror Hamiltonians

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Published in Journal of Modern Optics, 2021

Jake Southall, Daniel Hodgson, Robert Purdy, Almut Beige

Before analysing the dynamics associated with the mirror Hamiltonian in Equation (41), let us move from the Schrödinger into the interaction picture with respect to the free Hamiltonian and with respect to t = 0. In the following, denotes the state vector of the quantized EM field at time t in the interaction picture with being the corresponding state vector in the Schrödinger picture. As usual in physics, we define the state vector in the interaction picture such that Taking the time derivative of the above equation, one can show that this state vector evolves according to a Schrödinger equation but with the corresponding Hamiltonian given by In the absence of a mirror potential, at all times and local field excitations remain at their initial positions. The purpose of changing into the interaction picture is to simplify the following calculations by removing all free-space dynamics from the time evolution of the EM field.

Interaction picture

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An Introductory Review of Quantum Mechanics

Locally acting mirror Hamiltonians