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

2000/08/23 by T. Koide, M. Maruyama, Masahiro Maruyama · 4 citations
Computer Science · Physics and Astronomy · #Nonlinear Dynamics and Pattern Formation #Quantum Information and Cryptography #Spectroscopy and Quantum Chemical Studies #hep-th #nucl-th #quant-ph

paper · pdf · doi:10.1143/ptp.104.575

published as Prog.Theor.Phys. 104 (2000) 575-594 · 16 pages, revtex, no figures, To appear in Prog.Theor.Phys

arxiv created 2000/08/23 · openalex publication_date 2000/09/01 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We derive a new expansion of the Heisenberg equation of motion based on the projection operator method proposed by Shibata, Hashitsume and Shingū. 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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