Heisenberg and Interaction Representations

Alexander D. Sukhanov

Bian Qiu

The Heisenberg equation of motion of atom field interaction systems is formulated by the use of the representation of coherent state direct product. After introducting a newly defined operator amplitude fuction, the Heisenberg equation of motion for any operator is converted into partial differential equation of the type of separating variables. Formal solution of this differential equation is presented, and the time evolution operator is written down in the present representation.

Harry A. Mavromatis

Harry A. Mavromatis

Giancarlo Calvanese Strinati

In the Schrödinger and Heisenberg representations, the time-evolution operator depends on the full time-dependent Hamiltonian, which includes an external time-dependent potential. Out of this full-time dependence, it is useful to isolate the time dependences due to either the full system Hamiltonian or its noninteracting part. These two cases, referred to as the Heisenberg and interaction pictures, respectively, are considered separately.