open access

https://hdl.handle.net/2115/32287

HEISENBERG OPERATORS, INVARIANT DOMAINS AND HEISENBERG EQUATIONS OF MOTION

英語

Dirac operator

2007

World Scientific Publishing

Reviews in Mathematical Physics

19(10)

1045-1069

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.

学術雑誌論文

Accepted Manuscript

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

0129-055X