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HEISENBERG OPERATORS, INVARIANT DOMAINS AND HEISENBERG EQUATIONS OF MOTION
| Title: | HEISENBERG OPERATORS, INVARIANT DOMAINS AND HEISENBERG EQUATIONS OF MOTION |
| Authors: | Arai, Asao Browse this author →KAKEN DB |
| Keywords: | Heisenberg operator | | invariant domain | | Heisenberg equation of motion | | Schrodinger operator | | Dirac operator |
| Issue Date: | 2007 |
| Publisher: | World Scientific Publishing |
| Journal Title: | Reviews in Mathematical Physics |
| Volume: | 19 |
| Issue: | 10 |
| Start Page: | 1045 |
| End Page: | 1069 |
| Publisher DOI: | 10.1142/S0129055X07003206 |
| Abstract: | An abstract operator theory is developed on operators of the form A_{H}(t) := e^{itH}Ae^{-itH}, t ∈ R, with H a self-adjoint operator and A a linear operator on a Hilbert space (in the context of quantum mechanics, A_{H}(t) is called the Heisenberg operator of A with respect to H). The following aspects are discussed: (i) integral equations for A_{H}(t) for a general class of A; (ii) a sufficient condition for D(A), the domain of A, to be left invariant by e^{-itH} for all t ∈ R; (iii) a mathematically rigorous formulation of the Heisenberg equation of motion in quantum mechanics and the uniqueness of its solutions; (iv) invariant domains in the case where H is an abstract version of Schrödinger and Dirac operators; (v) applications to Schrödinger operators with matrix-valued potentials and Dirac operators. |
| Rights: | Electronic version of an article published as Reviews in Mathematical Physics, vol. 19, no. 10, 2007, 1045-1069, doi:10.1142/S0129055X07003206 (c) copyright World Scientific Publishing Company |
| Relation: | http://www.worldscinet.com/rmp/rmp.shtml |
| Type: | article (author version) |
| URI: | http://hdl.handle.net/2115/32287 |
| Appears in Collections: | 理学院・理学研究院 (Graduate School of Science / Faculty of Science) > 雑誌発表論文等 (Peer-reviewed Journal Articles, etc)
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Submitter: 新井 朝雄
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