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Spectrum of Time Operators
| Title: | Spectrum of Time Operators |
| Authors: | Arai, Asao Browse this author →KAKEN DB |
| Keywords: | Spectrum | | time operator | | Hamiltonian | | quantum theory | | weak Weyl relation |
| Issue Date: | Jun-2007 |
| Publisher: | Springer |
| Journal Title: | Letters in Mathematical Physics |
| Volume: | 80 |
| Issue: | 3 |
| Start Page: | 211 |
| End Page: | 221 |
| Publisher DOI: | 10.1007/s11005-007-0158-y |
| Abstract: | 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. |
| Rights: | The original publication is available at www.springerlink.com |
| Type: | article (author version) |
| URI: | http://hdl.handle.net/2115/32292 |
| 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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