open access

https://hdl.handle.net/2115/32292

Spectrum of Time Operators

英語

weak Weyl relation

2007-06

Springer

Letters in Mathematical Physics

80(3)

211-221

Let H be a self-adjoint operator on a complex Hilbert space H. A symmetric operator T on H is called a time operator of H if, for all t ∈ R, e^{-itH}D(T) ⊂ D(T) (D(T) denotes the domain of T) and Te^{-itH}ψ=e^{-itH}(T+t)ψ, ∀t ∈ R, ∀ψ ∈ D(T). In this paper, spectral properties of T are investigated. The following results are obtained: (i) If H is bounded below, then σ(T), the spectrum of T, is either C (the set of complex numbers) or {z ∈ C| Im z ≥ 0}. (ii) If H is bounded above, then σ(T) is either C or {z ∈ C| Im z ≤ 0}. (iii) If H is bounded, then σ(T)=C. The spectrum of time operators of free Hamiltonians for both nonrelativistic and relativistic particles is exactly identified. Moreover spectral analysis is made on a generalized time operator.

学術雑誌論文

Accepted Manuscript

The original publication is available at www.springerlink.com

0377-9017

1573-0530