Ultra-Weak Time Operators of Schrödinger Operators

Asao Arai, Fumio Hiroshima

研究成果: ジャーナルへの寄稿記事

抄録

In an abstract framework, a new concept on time operator, ultra-weak time operator, is introduced, which is a concept weaker than that of weak time operator. Theorems on the existence of an ultra-weak time operator are established. As an application of the theorems, it is shown that Schrödinger operators HV with potentials V obeying suitable conditions, including the Hamiltonian of the hydrogen atom, have ultra-weak time operators. Moreover, a class of Borel measurable functions f: R→ R such that f(HV) has an ultra-weak time operator is found.

元の言語英語
ページ(範囲)2995-3033
ページ数39
ジャーナルAnnales Henri Poincare
18
発行部数9
DOI
出版物ステータス出版済み - 9 1 2017

Fingerprint

Time Operator
operators
Operator
Borel Functions
theorems
Hydrogen Atom
Measurable function
Theorem
hydrogen atoms

All Science Journal Classification (ASJC) codes

  • Statistical and Nonlinear Physics
  • Nuclear and High Energy Physics
  • Mathematical Physics

これを引用

Ultra-Weak Time Operators of Schrödinger Operators. / Arai, Asao; Hiroshima, Fumio.

:: Annales Henri Poincare, 巻 18, 番号 9, 01.09.2017, p. 2995-3033.

研究成果: ジャーナルへの寄稿記事

Arai, Asao ; Hiroshima, Fumio. / Ultra-Weak Time Operators of Schrödinger Operators. :: Annales Henri Poincare. 2017 ; 巻 18, 番号 9. pp. 2995-3033.
@article{c4f6dd4e5009460d808fbb5a25e421d0,
title = "Ultra-Weak Time Operators of Schr{\"o}dinger Operators",
abstract = "In an abstract framework, a new concept on time operator, ultra-weak time operator, is introduced, which is a concept weaker than that of weak time operator. Theorems on the existence of an ultra-weak time operator are established. As an application of the theorems, it is shown that Schr{\"o}dinger operators HV with potentials V obeying suitable conditions, including the Hamiltonian of the hydrogen atom, have ultra-weak time operators. Moreover, a class of Borel measurable functions f: R→ R such that f(HV) has an ultra-weak time operator is found.",
author = "Asao Arai and Fumio Hiroshima",
year = "2017",
month = "9",
day = "1",
doi = "10.1007/s00023-017-0586-x",
language = "English",
volume = "18",
pages = "2995--3033",
journal = "Annales Henri Poincare",
issn = "1424-0637",
publisher = "Birkhauser Verlag Basel",
number = "9",

}

TY - JOUR

T1 - Ultra-Weak Time Operators of Schrödinger Operators

AU - Arai, Asao

AU - Hiroshima, Fumio

PY - 2017/9/1

Y1 - 2017/9/1

N2 - In an abstract framework, a new concept on time operator, ultra-weak time operator, is introduced, which is a concept weaker than that of weak time operator. Theorems on the existence of an ultra-weak time operator are established. As an application of the theorems, it is shown that Schrödinger operators HV with potentials V obeying suitable conditions, including the Hamiltonian of the hydrogen atom, have ultra-weak time operators. Moreover, a class of Borel measurable functions f: R→ R such that f(HV) has an ultra-weak time operator is found.

AB - In an abstract framework, a new concept on time operator, ultra-weak time operator, is introduced, which is a concept weaker than that of weak time operator. Theorems on the existence of an ultra-weak time operator are established. As an application of the theorems, it is shown that Schrödinger operators HV with potentials V obeying suitable conditions, including the Hamiltonian of the hydrogen atom, have ultra-weak time operators. Moreover, a class of Borel measurable functions f: R→ R such that f(HV) has an ultra-weak time operator is found.

UR - http://www.scopus.com/inward/record.url?scp=85019598711&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85019598711&partnerID=8YFLogxK

U2 - 10.1007/s00023-017-0586-x

DO - 10.1007/s00023-017-0586-x

M3 - Article

AN - SCOPUS:85019598711

VL - 18

SP - 2995

EP - 3033

JO - Annales Henri Poincare

JF - Annales Henri Poincare

SN - 1424-0637

IS - 9

ER -