Heisenberg Equations Approach

Julio César Jaramillo Quiceno

In this paper we introduce the $q$-deformed Heisenberg picture equation. We consider some examples such as : the spinless particle, the electrón interaction with a magnnetic field and $q$-deformed harmonnic oscillator. The $q$-Heisenberg picture equation for any dynamical function at the end of the paper.

Shue-Kwing Chan, Kiang-Chuen Young

G. F. Torres del Castillo

It is shown that the knowledge of the solution of the Heisenberg equations for a given Hamiltonian allows us to find the corresponding propagator up to a time-dependent phase factor, which gives the solution of the Schrödinger equation.

Vasily Evgenevich Tarasov

Harry A. Mavromatis

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.