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Mathematical Analysis of Quantum Physics

Research Project

Project/Area Number 22340029
Research Category

Grant-in-Aid for Scientific Research (B)

Allocation TypeSingle-year Grants
Section一般
Research Field Basic analysis
Research InstitutionGakushuin University

Principal Investigator

YAJIMA Kenji  学習院大学, 理学部, 教授 (80011758)

Project Period (FY) 2010-04-01 – 2015-03-31
Project Status Completed (Fiscal Year 2014)
Budget Amount *help
¥13,390,000 (Direct Cost: ¥10,300,000、Indirect Cost: ¥3,090,000)
Fiscal Year 2014: ¥2,600,000 (Direct Cost: ¥2,000,000、Indirect Cost: ¥600,000)
Fiscal Year 2013: ¥2,600,000 (Direct Cost: ¥2,000,000、Indirect Cost: ¥600,000)
Fiscal Year 2012: ¥2,600,000 (Direct Cost: ¥2,000,000、Indirect Cost: ¥600,000)
Fiscal Year 2011: ¥2,600,000 (Direct Cost: ¥2,000,000、Indirect Cost: ¥600,000)
Fiscal Year 2010: ¥2,990,000 (Direct Cost: ¥2,300,000、Indirect Cost: ¥690,000)
Keywordsシュレーディンガー方程式 / 初期値問題 / 散乱理論 / 波動作用素 / 量子力学 / 偏微分方程式 / 数理物理学 / 関数解析 / 散乱の波動作用素 / ルベーグ空間 / 分散型評価 / シュレーディンガ方程式 / 関数方程式 / シュレーディンガー作用素 / 関数解析学 / 作用素論 / 微分方程式 / スペクトル理論 / 漸近展開 / 重み付きアマルガム空間 / 極限吸収原理 / 解作用素 / 本質的自己共役性
Outline of Final Research Achievements

Small particles like electrons and atoms are described by quantum mechanics and their dynamics is governed by Schrodinger equations which are partial differential equations for complex valued functions. The reporter studied the initial value problem for Schrodinger equations and, he has found very general sufficient conditions on inter-particle and external forces acting on the particles for the equation to generate a unique dynamics of the particles. The wave operators of the scattering theory for the Schrodinger equations, which describe the large time behavior of the particles, play important roles in various other topics of analysis. The reporter simultaneously studied the wave operators and has found various mathematically important properties such as the continuity as mapping from suitable function spaces.

Report

(6 results)
  • 2014 Annual Research Report   Final Research Report ( PDF )
  • 2013 Annual Research Report
  • 2012 Annual Research Report
  • 2011 Annual Research Report
  • 2010 Annual Research Report
  • Research Products

    (42 results)

All 2015 2014 2013 2012 2011 2010 Other

All Journal Article (13 results) (of which Peer Reviewed: 11 results,  Acknowledgement Compliant: 3 results) Presentation (27 results) (of which Invited: 16 results) Book (2 results)

  • [Journal Article] Schrodinger equations with time-dependent strong magnetic fields2014

    • Author(s)
      D. Aiba and K. Yajima
    • Journal Title

      St. Petersburg Mathematical Journal

      Volume: 25 Pages: 175-194

    • Related Report
      2014 Annual Research Report
    • Peer Reviewed / Acknowledgement Compliant
  • [Journal Article] Dispersive estimates for Schrodinger equations2014

    • Author(s)
      K. Yajima
    • Journal Title

      Sugaku Expositions

      Volume: 27 Pages: 147-174

    • Related Report
      2014 Annual Research Report
    • Peer Reviewed / Acknowledgement Compliant
  • [Journal Article] Resolvent estimates in amalgam spaces and asymptotic expansions for Schrödinger equations2014

    • Author(s)
      A. Galtbayar and K. Yajima
    • Journal Title

      RIMS Kokyuroku Bessatsu

      Volume: B45 Pages: 113-130

    • Related Report
      2014 Annual Research Report
    • Acknowledgement Compliant
  • [Journal Article] Resolvent estimates in amalgam space and asymptotic expansions for Schroedinger equations2014

    • Author(s)
      A. Galtbayar, 谷島賢二
    • Journal Title

      RIMS Kokyuroku Bessatsu

      Volume: 54 Pages: 113-130

    • Related Report
      2013 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Dispersive estimates for Schroedinger equations2014

    • Author(s)
      Kenji Yajima
    • Journal Title

      Sugku Expositions

      Volume: 未定

    • Related Report
      2012 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Schroedinger equations with time-dependent strong magnetic fields.2014

    • Author(s)
      Daisuke Aiba, Kenji Yajima
    • Journal Title

      St. Petersburg Mathematical Journal

      Volume: 25 Pages: 175-194

    • Related Report
      2012 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Resolvent estimates in amalgam spaces and asymptotic expansions for Schrödinger equations2013

    • Author(s)
      Artbazar Galtbayar
    • Journal Title

      Journal of the Mathematical Society of Japan

      Volume: 65 Issue: 2 Pages: 563-605

    • DOI

      10.2969/jmsj/06520563

    • NAID

      10031177291

    • ISSN
      0025-5645, 1881-1167, 1881-2333
    • Related Report
      2012 Annual Research Report 2011 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Schrodinger equations with time-dependent strong magnetic potentials2013

    • Author(s)
      Daisuke Aiba
    • Journal Title

      Algebra and Analysis

      Volume: 25 Pages: 39-63

    • Related Report
      2011 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Schroedinger equations with time-dependent unbounded singular potentials2011

    • Author(s)
      Kenji Yajima
    • Journal Title

      Revies in Mathematical Physics

      Volume: 23 Issue: 08 Pages: 823-838

    • DOI

      10.1142/s0129055x11004436

    • Related Report
      2011 Annual Research Report
    • Peer Reviewed
  • [Journal Article] シュレーディンガー方程式の分散型評価2010

    • Author(s)
      谷島賢二
    • Journal Title

      日本数学会機関誌「数学」

      Volume: 62 Pages: 145-163

    • NAID

      130004558905

    • Related Report
      2010 Annual Research Report
    • Peer Reviewed
  • [Journal Article] 調和振動子のある摂動の基本解の非有界性2010

    • Author(s)
      谷島賢二
    • Journal Title

      京都大学数理解析研究所講究録

      Volume: 1696 Pages: 144-157

    • Related Report
      2010 Annual Research Report
  • [Journal Article] Lifshitz tails for generalized alloy type random Schroedinger operators2010

    • Author(s)
      Klopp, F.Shu Nakamura
    • Journal Title

      Analysis and Partial differential equations

      Volume: 3 Pages: 409-426

    • Related Report
      2010 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Time-dependent scattering theory for Schroedinger operators on scattering manifolds2010

    • Author(s)
      Ito, K., Shu Nakamura
    • Journal Title

      Journal of London Mathematical Society

      Volume: 81 Pages: 774-792

    • Related Report
      2010 Annual Research Report
    • Peer Reviewed
  • [Presentation] 波動作用素のL-p有界性について2014

    • Author(s)
      谷島賢二
    • Organizer
      研究集会「第25回数理物理と微分方程式」
    • Place of Presentation
      四季の湯「強羅青雲荘」
    • Year and Date
      2014-11-01 – 2014-11-03
    • Related Report
      2014 Annual Research Report
  • [Presentation] L p -boundedness of wave operators, revisited2014

    • Author(s)
      谷島 賢二
    • Organizer
      RIMS研究集会「スペクトル・散乱理論とその周辺」
    • Place of Presentation
      京都大学数理解析研究所
    • Year and Date
      2014-10-15 – 2014-10-17
    • Related Report
      2014 Annual Research Report
    • Invited
  • [Presentation] Hydrogen-like atoms in semi-classical electro-magnetic fields2014

    • Author(s)
      谷島 賢二
    • Organizer
      RIMS研究集会「量子場の数理とその周辺」
    • Place of Presentation
      京都大学数理解析研究所
    • Year and Date
      2014-10-06 – 2014-10-08
    • Related Report
      2014 Annual Research Report
    • Invited
  • [Presentation] L^p boundedness of wave operators for Schrodinger operators with threshold singularities2014

    • Author(s)
      K. Yajima
    • Organizer
      Aarhus university Mathematical Physics Meeting
    • Place of Presentation
      Aarhus 大学(デンマーク)
    • Year and Date
      2014-08-20
    • Related Report
      2014 Annual Research Report
    • Invited
  • [Presentation] 波動作用素のL^p有界性について2013

    • Author(s)
      谷島 賢二
    • Organizer
      研究集会第24回「数理物理と微分方程式」
    • Place of Presentation
      星と森のロマントピア(弘前市)
    • Related Report
      2013 Annual Research Report
  • [Presentation] Existence of propagators for Schroedinger equations with strong magnetic fields2012

    • Author(s)
      谷島」賢二
    • Organizer
      Conference "Mathematics of multi-particle systems"
    • Place of Presentation
      ベルリン工科大学
    • Related Report
      2012 Annual Research Report
    • Invited
  • [Presentation] Schroedinger equation with strong magnetic fields2012

    • Author(s)
      谷島 賢二
    • Organizer
      研究集会「数理物理と微分方程式」
    • Place of Presentation
      国民宿舎「野呂高原ロッジ」
    • Related Report
      2012 Annual Research Report
  • [Presentation] Resolvent Estimates in Amalgam Spaces and Asymptotic Expansions for Schreodinger Equations2012

    • Author(s)
      Kenji Yajima
    • Organizer
      Mathematical Physics Seminar
    • Place of Presentation
      University of Muenchen
    • Related Report
      2011 Annual Research Report
    • Invited
  • [Presentation] Existence and uniqueness of propagator for Schrödinger equations with strong magnetic fields2012

    • Author(s)
      Kenji Yajima
    • Organizer
      Mathematics of Many-Particle Systems
    • Place of Presentation
      Technical University of Berlin
    • Related Report
      2011 Annual Research Report
    • Invited
  • [Presentation] Dispersive estimates for Schr¨odinger equations , I, II2012

    • Author(s)
      谷島賢二
    • Organizer
      調和解析と非線形偏微分方程式
    • Place of Presentation
      京都大学数理解析研究所
    • Related Report
      2011 Annual Research Report
    • Invited
  • [Presentation] Schroedinger equations with strong magnetic fields2012

    • Author(s)
      谷島賢二
    • Organizer
      第23回研究集会「数理物理と微分方程式」
    • Place of Presentation
      国民宿舎 野呂高原ロッジ
    • Related Report
      2011 Annual Research Report
  • [Presentation] Existence and uniquenwess of propagators for Schroedinger equations2012

    • Author(s)
      Kenji Yajima
    • Organizer
      Workshop on "Scvhroedinger operators with magnetic fields"
    • Place of Presentation
      Mittag-Leffler Institute
    • Related Report
      2011 Annual Research Report
    • Invited
  • [Presentation] Resolvent estimates in Amalgam spaces and asymptotic expansions for Schroedinger equations2011

    • Author(s)
      Kenji Yajima
    • Organizer
      Mathematical Physics Seminar
    • Place of Presentation
      チューリッヒ工科大学Zurich, Switzerland(招待講演)
    • Year and Date
      2011-02-25
    • Related Report
      2010 Annual Research Report
  • [Presentation] Resolvent estimates in Amalgam spaces and asymptotic expansions for Schroedinger equations2011

    • Author(s)
      Kenji Yajima
    • Organizer
      Mathematical Physics Seminar
    • Place of Presentation
      ボローニャ大学数学科Bologna, Italy(招待講演)
    • Year and Date
      2011-02-23
    • Related Report
      2010 Annual Research Report
  • [Presentation] Resolvent estimates in Amalgam spaces and asymptotic expansions for Schroedinger equations2011

    • Author(s)
      Kenji Yajima
    • Organizer
      Mathematical Physics Sector Seminar
    • Place of Presentation
      SISSA, Trieste, Italy(招待講演)
    • Year and Date
      2011-02-21
    • Related Report
      2010 Annual Research Report
  • [Presentation] Resolvent Estimates in Amalgam Spaces and Asymptotic Expansions for Schreodinger Equations2011

    • Author(s)
      Kenji Yajima
    • Organizer
      Scattering Theory: An International Workshop in Tokyo, 2011
    • Place of Presentation
      東京大学大学院数理科学研究科
    • Related Report
      2011 Annual Research Report
    • Invited
  • [Presentation] Selfadjointness of Schreodinger operators with potentials with critical singularities2011

    • Author(s)
      谷島賢二
    • Organizer
      第22回研究集会「数理物理と微分方程式」
    • Place of Presentation
      ヒルズサンピア山形
    • Related Report
      2011 Annual Research Report
  • [Presentation] Resolvent Estimates in Amalgam Spaces and Asymptotic Expansions for Schrodinger Equations2011

    • Author(s)
      谷島賢二
    • Organizer
      研究集会「スペクトル・散乱理論とその周辺」
    • Place of Presentation
      京都大学数理解析研究所
    • Related Report
      2011 Annual Research Report
    • Invited
  • [Presentation] On dispersive estimates on Schroedinger equations2010

    • Author(s)
      谷島賢二
    • Organizer
      「早稲田大学非線形偏微分方程式研究所」設立研究集会
    • Place of Presentation
      早稲田大学理工学部(招待講演)
    • Year and Date
      2010-11-11
    • Related Report
      2010 Annual Research Report
  • [Presentation] On dispersive estimates on Schroedinger equations2010

    • Author(s)
      谷島賢二
    • Organizer
      東北大学理学部数学科談話会
    • Place of Presentation
      東北大学理学部(招待講演)
    • Year and Date
      2010-10-18
    • Related Report
      2010 Annual Research Report
  • [Presentation] On dispersive estimates on Schroedinger equations2010

    • Author(s)
      谷島賢二
    • Organizer
      第35回札幌偏微分方程式研究集会
    • Place of Presentation
      北海道大学理学部(招待講演)
    • Year and Date
      2010-08-23
    • Related Report
      2010 Annual Research Report
  • [Presentation] Existence and uniqueness of the propagator for Schroedinger equations with exploding magnetic potentials

    • Author(s)
      谷島 賢二
    • Organizer
      Mat/Fys-seminar
    • Place of Presentation
      Aarhus 大学(デンマーク)
    • Related Report
      2013 Annual Research Report
    • Invited
  • [Presentation] Resolvent estimates in Amalgam spaces and asymptotic expansions for Schroedinger equations

    • Author(s)
      谷島 賢二
    • Organizer
      Oberseminar Mathematische Physik
    • Place of Presentation
      ミュンヘン大学数学科
    • Related Report
      2012 Annual Research Report
    • Invited
  • [Presentation] Propoagatror for Schreodinger equations with strong magnetic fields

    • Author(s)
      谷島 賢二
    • Organizer
      Workship "Schroedinger op@erators with magnetic fields"
    • Place of Presentation
      Mittag-Leffler Institute of Mathematics
    • Related Report
      2012 Annual Research Report
    • Invited
  • [Presentation] Resolvent Estimates in Amalgam Spaces and Asymptotic Expansions for Schreodinger Equations

    • Author(s)
      谷島賢二
    • Organizer
      北九州解析学セミナー
    • Place of Presentation
      福岡大学セミナーハウス
    • Related Report
      2011 Annual Research Report
    • Invited
  • [Presentation] Schreodinger equations with time dependent unbounded singular potentials

    • Author(s)
      谷島賢二
    • Organizer
      応用解析研究会
    • Place of Presentation
      早稲田大学理工学術院
    • Related Report
      2011 Annual Research Report
    • Invited
  • [Presentation] Existence and Uniqueness of the Propagator for time dependent Schroedinger equations

    • Author(s)
      Kenji Yajima
    • Organizer
      Colloquium Talk at Math. Department of Technical University Braunschweig
    • Place of Presentation
      Technical University Braunchweig
    • Related Report
      2011 Annual Research Report
    • Invited
  • [Book] シュレーディンガー方程式1,ならびに22015

    • Author(s)
      谷島 賢二
    • Total Pages
      594
    • Publisher
      朝倉書店
    • Related Report
      2014 Annual Research Report
  • [Book] シュレーディンガー方程式 1, ならびに 22014

    • Author(s)
      谷島 賢二
    • Total Pages
      640
    • Publisher
      朝倉書店
    • Related Report
      2013 Annual Research Report

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Published: 2010-08-23   Modified: 2019-07-29  

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