A New Expansion of the Heisenberg Equation of Motion with Projection Operator

Details A New Expansion of the Heisenberg Equation of Motion with Projection Operator A New Expansion of the Heisenberg Equation of Motion with Projection Operator

2000-08-23

arxiv.org/abs/hep-th/0008182v1

Prog.Theor.Phys. 104 (2000) 575-594

Physics

High Energy Physics

High Energy Physics - Theory

16 pages, revtex, no figures, To appear in Prog.Theor.Phys

Scientific paper

10.1143/PTP.104.575

We derive a new expansion of the Heisenberg equation of motion based on the projection operator method proposed by Shibata, Hashitsume and Shing\=u. In their projection operator method, a certain restriction is imposed on the initial state. As a result, one cannot prepare arbitrary initial states, for example a coherent state, to calculate the time development of quantum systems. In this paper, we generalize the projection operator method by relaxing this restriction. We explain our method in the case of a Hamiltonian both with and without explicit time dependence. Furthermore, we apply it to an exactly solvable model called the damped harmonic oscillator model and confirm the validity of our method.

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