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Mathematical Analysis of Quantum Physics

Research Project

Project/Area Number 18340041
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 (KENJI Yajima)  Gakushuin University, 理学部, 教授 (80011758)

Co-Investigator(Kenkyū-buntansha) FUJIWARA Daisuke  学習院大学, 理学部, 教授 (10011561)
NAKAMURA Shu  東京大学, 大学院・数理科学研究科, 教授 (50183520)
MIZUTANI Akira  学習院大学, 理学部, 教授 (80011716)
WATANABE Kazuo  学習院大学, 理学部, 助教 (90260851)
SHIMOMURA Akihiro  首都大学東京, 大学院・理工学研究科, 准教授 (00365066)
Project Period (FY) 2006 – 2009
Project Status Completed (Fiscal Year 2009)
Budget Amount *help
¥10,000,000 (Direct Cost: ¥8,200,000、Indirect Cost: ¥1,800,000)
Fiscal Year 2009: ¥2,600,000 (Direct Cost: ¥2,000,000、Indirect Cost: ¥600,000)
Fiscal Year 2008: ¥2,600,000 (Direct Cost: ¥2,000,000、Indirect Cost: ¥600,000)
Fiscal Year 2007: ¥2,600,000 (Direct Cost: ¥2,000,000、Indirect Cost: ¥600,000)
Fiscal Year 2006: ¥2,200,000 (Direct Cost: ¥2,200,000)
Keywords関数方程式 / 関数解析 / 実解析 / 量子力学 / シュレーディンガー作用素 / シュレーディンガー方程式 / 線形偏微分方程式 / 散乱理論 / 特異性伝播 / ファインマン経路積分 / スペクトル理論 / 数理物理学 / 関数解析学 / 偏微分方程式 / 基本解 / 経路積分 / 量子物理学 / 特異性伝播問題 / 非線形偏微分方程式 / 分散型評価 / 非線形方程式
Research Abstract

We studied mathematical problems on Schroedinger equations which are fundamental equation for describing the dynamics of quantum particles and obtained following results : (1) New results are obtained on the behavior at infinity of the fundamental solutions of the initial value problems ; (2) new methods for studying the propagation of singularities of solutions are found ; (3) unsolved problems on wave operators of scattering have been solved ; (4) new spectral properties of random Schroedinger operators are found.

Report

(6 results)
  • 2009 Annual Research Report   Final Research Report ( PDF )
  • 2008 Annual Research Report   Self-evaluation Report ( PDF )
  • 2007 Annual Research Report
  • 2006 Annual Research Report
  • Research Products

    (91 results)

All 2010 2009 2008 2007 2006 Other

All Journal Article (51 results) (of which Peer Reviewed: 41 results) Presentation (38 results) Book (2 results)

  • [Journal Article] Spatial growth of fundamental solutions for certain perturbations of the harmonic oscillator2010

    • Author(s)
      A. Jensen, K. Yajima
    • Journal Title

      Review in Mathematical Physics 22

      Pages: 193-206

    • Related Report
      2009 Final Research Report
    • Peer Reviewed
  • [Journal Article] Spatial growth of fundamental solutions for certain perturbations of the harmonic oscillator2010

    • Author(s)
      A.Jensen, K.Yajima
    • Journal Title

      Reviews in Mathematical Physics 22

      Pages: 193-206

    • Related Report
      2009 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Semiclassical singularity propagation property for Schroedinger equations.2009

    • Author(s)
      S. Nakamura
    • Journal Title

      Journal of the Mathematical Society of Japan 61

      Pages: 177-211

    • Related Report
      2009 Final Research Report
    • Peer Reviewed
  • [Journal Article] Spectral extrema and Lifshitz tails for non monotonous alloy type models.2009

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

      Commun. in Mathematical Physics 287

      Pages: 1133-1143

    • Related Report
      2009 Final Research Report
    • Peer Reviewed
  • [Journal Article] Analytic wave front for solutions to Schroedinger equation2009

    • Author(s)
      A. Martnez, S. Nakamura, B.V. Sordoni
    • Journal Title

      Advances in Mathematics 222

      Pages: 1277-1307

    • Related Report
      2009 Final Research Report
    • Peer Reviewed
  • [Journal Article] Singularities of solutions to Schroedinger equation on scattering manifold.2009

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

      American Journal of Mathematics 131

      Pages: 1835-1865

    • Related Report
      2009 Final Research Report
    • Peer Reviewed
  • [Journal Article] Wave front set for solutions to Schroedeinger equations2009

    • Author(s)
      S. Nakamura
    • Journal Title

      Journal of Functional analysis 256

      Pages: 1299-1309

    • Related Report
      2009 Final Research Report
    • Peer Reviewed
  • [Journal Article] Semi-classical singularity propagation property for Schrodinger equations.2009

    • Author(s)
      S.Nakamura
    • Journal Title

      Journal of the Mathematical Society of Japan 61

      Pages: 177-211

    • Related Report
      2009 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Spectral extrema and Lifshitz tails for non monotonous alloy type models.2009

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

      Communication in Mathematical Physics 287

      Pages: 1133-1143

    • Related Report
      2009 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Wave front set for solutions to perturbed harmonic oscillators.2009

    • Author(s)
      S.Mao, S.Nakamuara
    • Journal Title

      Communications in Partial Differential Equations 34

      Pages: 506-519

    • Related Report
      2009 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Analytic wave front for solutions to Schrodinger equation2009

    • Author(s)
      A.Martnez, S.Nakamura, B.V.Sordoni
    • Journal Title

      Advancess in Mathematics 222

      Pages: 1277-1307

    • Related Report
      2009 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Singularities of solutions to Schrodinger equation on scattering manifold.2009

    • Author(s)
      K.Ito, S.Nakamuar
    • Journal Title

      American Journal of Mathematics 131

      Pages: 1835-1865

    • Related Report
      2009 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Wave front set for solutions to Schroedinger equations2009

    • Author(s)
      Shu Nakamura
    • Journal Title

      J. Funct. Anal Vol.256

      Pages: 1299-1309

    • Related Report
      2008 Self-evaluation Report
    • Peer Reviewed
  • [Journal Article] Wave front set for solutions to Schroedeinger equations2009

    • Author(s)
      S.Nakamura
    • Journal Title

      Journal of Functional analysis 256

      Pages: 1299-1309

    • Related Report
      2008 Annual Research Report
    • Peer Reviewed
  • [Journal Article] On L^p boundedness of wave operators for 4-dimensional Schroedinger operators with threshold singularities2008

    • Author(s)
      A. Jensen, K. Yajima
    • Journal Title

      Proceedings of London Mathematical Society 96(3)

      Pages: 136-162

    • Related Report
      2009 Final Research Report
    • Peer Reviewed
  • [Journal Article] Analytic singularities for long range Schroedinger equations2008

    • Author(s)
      A. Martinez, S. Nakamura, V. Sordoni
    • Journal Title

      Comptes Randus Mathematiques 346

      Pages: 859-852

    • Related Report
      2009 Final Research Report
    • Peer Reviewed
  • [Journal Article] Phase space Feynman path integrals via piecewise bicharacteristic paths and their semi-classical approximations2008

    • Author(s)
      N. Kumano-go, D. Fujiwara
    • Journal Title

      Bulletin des Sciences Mathematiques 132

      Pages: 313-357

    • Related Report
      2009 Final Research Report
    • Peer Reviewed
  • [Journal Article] Phase space Feynman path integral via piecewise bicharacteristic paths and their semi-classical approximations2008

    • Author(s)
      Naoto Kumano-go, Daisuke Fujiwara
    • Journal Title

      Bull. Sci. Math vol.132

      Pages: 313-357

    • Related Report
      2008 Self-evaluation Report
    • Peer Reviewed
  • [Journal Article] On L^p boundedness of wave operators for 4-dimensional Schroedinger operators with threshold singularities2008

    • Author(s)
      A.Jensen, K.Yajima
    • Journal Title

      Proceedings of London Mathematical Society(3) 96

      Pages: 136-162

    • Related Report
      2008 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Analytic singularities for long range Schroedinger equations2008

    • Author(s)
      A.Martinez, S.Nakamura, V.Sordoni
    • Journal Title

      Comptes Randus Mathematiques 346

      Pages: 859-852

    • Related Report
      2008 Annual Research Report
    • Peer Reviewed
  • [Journal Article] On L^p boundeness of wave operators for four dimensional Schrodinger operators with threshold singularities2008

    • Author(s)
      Arne Jensen
    • Journal Title

      Proceeding of the London Mathematical Society 96

      Pages: 136-162

    • Related Report
      2007 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Phase space Feynman path integrals via piecewise bicharacteristic paths and their semiclassical approximations,2008

    • Author(s)
      Naoto Kumano-go
    • Journal Title

      Bulletin des Sciences Mathematiques (In press)

    • Related Report
      2007 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Asymptotic behavior of solutions to Schroedinger equations with a subcritical dissipative nonlinearity2007

    • Author(s)
      N. Kita, A. Shimomura
    • Journal Title

      Journal of Differential Equations 242

    • Related Report
      2009 Final Research Report
    • Peer Reviewed
  • [Journal Article] Scattering theory for the Schroedinger-improved Boussinesq system in two space dimensions2007

    • Author(s)
      A. Shimomura
    • Journal Title

      Asymptotic Analysis 51

      Pages: 167-187

    • Related Report
      2009 Final Research Report
    • Peer Reviewed
  • [Journal Article] Non-selfadjoint perturbation of Schroedinger and wave equations2007

    • Author(s)
      M. Kadowaki, K. Watanabe
    • Journal Title

      Advanced Studies and Pure Mathematics 47

      Pages: 137-157

    • Related Report
      2009 Final Research Report
    • Peer Reviewed
  • [Journal Article] Asymptotic behavior of solutions to Schrodinger equations with a subcritical dissipative nonlinearity2007

    • Author(s)
      Naoyasu Kita
    • Journal Title

      Journal of Differential Equations 242

      Pages: 192-210

    • Related Report
      2007 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Scattering theory for the Schrodinger-improved Boussinesq system in two space dimensions2007

    • Author(s)
      Akihiro Shimomura
    • Journal Title

      Asymptotic Analysis 51

      Pages: 167-187

    • Related Report
      2007 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Global existence and asymptotic behavior of solution to the fourth order nonlinear Schrodinger type equation2007

    • Author(s)
      Jun Segata
    • Journal Title

      Communications in Applied Analysis Vol.11 11

      Pages: 169-188

    • Related Report
      2007 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Non-selfadjoint perturbation of Schr\"odinger and wave equations, pp.2007

    • Author(s)
      M.Kadowaki
    • Journal Title

      Advanced Studies and Pure Math. 47

      Pages: 137-157

    • Related Report
      2007 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Some results on spectral analysis of non-selfadjoint perturbati on for Schrodinger and wave equations,2007

    • Author(s)
      M.Kadowaki
    • Journal Title

      Proceedings of 6'th ISAAC congress, To appear

    • Related Report
      2007 Annual Research Report
  • [Journal Article] The L^p boundedness of wave operators with threshold singularities I, Odd dimensional case2006

    • Author(s)
      K. Yajima
    • Journal Title

      Journal of Mathematical Sciences, University of Tokyo 13

      Pages: 43-93

    • Related Report
      2009 Final Research Report
    • Peer Reviewed
  • [Journal Article] The L^p boundedness of wave operators with threshold singularities II, Even dimensional case2006

    • Author(s)
      D. Finco, K. Yajima
    • Journal Title

      Journal of Mathematical Sciences, University of Tokyo 13

      Pages: 277-346

    • Related Report
      2009 Final Research Report
    • Peer Reviewed
  • [Journal Article] Analytic smoothing effect for the Schroedinger equations with long range perturbation2006

    • Author(s)
      A. Martinez, S. Nakamura, V. Sordoni
    • Journal Title

      Communications in Pure and Applied Mathematics 59

      Pages: 1330-1361

    • Related Report
      2009 Final Research Report
    • Peer Reviewed
  • [Journal Article] Bounds on spectral shift functions and the density of states2006

    • Author(s)
      D. Hundredmark, R. Killip, S. Nakamura, P. Stollmann, I. Veselic
    • Journal Title

      Communications in Mathematical Physic 262

    • Related Report
      2009 Final Research Report
    • Peer Reviewed
  • [Journal Article] Asymptotic behavior of solutions of Schroedinger equations with dissipative nonlinearities2006

    • Author(s)
      A. Shimomura
    • Journal Title

      Commun. in Partial Differential Equations 31

      Pages: 1407-1423

    • Related Report
      2009 Final Research Report
    • Peer Reviewed
  • [Journal Article] Nonexistence of scattering states for some quadratic nonlinear Schroedinger equation in two space dimensions2006

    • Author(s)
      A. Shimomura, Y. Tsutsumi
    • Journal Title

      Differential and Integral Equation 19

      Pages: 1047-1060

    • Related Report
      2009 Final Research Report
    • Peer Reviewed
  • [Journal Article] An improved remainder estimates of stationary phase method for some oscillatory integrals over a space of large dimensions2006

    • Author(s)
      D. Fujiwara, N. Kumano-go
    • Journal Title

      Funkcilaj Ekvacioj 49

      Pages: 59-86

    • NAID

      130000140660

    • Related Report
      2009 Final Research Report
    • Peer Reviewed
  • [Journal Article] The second term of semi-classical expansion for Feynman path integrals with integrand of polynomial growth2006

    • Author(s)
      D. Fujiwara, N. Kumano-g
    • Journal Title

      Journal of the Mathematical Society of Japan 58

      Pages: 847-867

    • Related Report
      2009 Final Research Report
    • Peer Reviewed
  • [Journal Article] The L^p boundednes of wave operators for Schroedinger operators with threshold singularities I, Odd dimensional case2006

    • Author(s)
      Kenji Yajima
    • Journal Title

      J. Math. Sci vol. 13

      Pages: 43-93

    • Related Report
      2008 Self-evaluation Report
    • Peer Reviewed
  • [Journal Article] The L^p boundednes of wave operators for Schroedinger operators with threshold singularities II, Even dimensional case2006

    • Author(s)
      Domenico Finco, Kenji Yajima
    • Journal Title

      J. Math. Sci Univ. Tokyo vol. 13

      Pages: 277-356

    • Related Report
      2008 Self-evaluation Report
    • Peer Reviewed
  • [Journal Article] Analytic smoothing effect for Schroedinger equations with long range perturbation2006

    • Author(s)
      Andre Martinez, Shu Nakamura, VaniaSordoni
    • Journal Title

      Comm. Pure. Appl. Math vol. 59

      Pages: 1330-1361

    • Related Report
      2008 Self-evaluation Report
    • Peer Reviewed
  • [Journal Article] the L^p boundedness of wave operators for Schroedinger operators with threshold singularities I, Odd dimensional case2006

    • Author(s)
      Yajima, K.
    • Journal Title

      Journal of Mathematical Sciences, University of Tokyo 13/1

      Pages: 43-93

    • Related Report
      2006 Annual Research Report
  • [Journal Article] The L^p boundedness of wave operators for Schroedinger operators with threshold singularities II, Even dimensional case2006

    • Author(s)
      Fince, D., Yajima, K.
    • Journal Title

      Journal of Mathematical Sciences, University of Tokyo 13/2

      Pages: 277-346

    • Related Report
      2006 Annual Research Report
  • [Journal Article] Analytic smoothing effect for the Schroedinger equations with long range perturbation2006

    • Author(s)
      Martinez, A., Nakamura, S., Sordoni, W.
    • Journal Title

      Communications on Pure and applied Mathematics 59/9

      Pages: 1330-1361

    • Related Report
      2006 Annual Research Report
  • [Journal Article] Bounds on spectral shift functions and the density of states2006

    • Author(s)
      Hundredmark, D., Killip, R., Nakamura, S., Stollann, P, Veselic, I.
    • Journal Title

      Communications in Mathematical Physics 262

      Pages: 489-503

    • Related Report
      2006 Annual Research Report
  • [Journal Article] asymptotic behavior of solutions of Schroedinger equations with dissipative nonlineraties2006

    • Author(s)
      Shimomura, A.
    • Journal Title

      Communications in Partial Differential Equations 31

      Pages: 1407-1423

    • Related Report
      2006 Annual Research Report
  • [Journal Article] Nonexistence of scattering states for some quadratic nonlinera Schreodinger equation in tow space dimensions2006

    • Author(s)
      Shimomura, A., Tsutsumi, Y.
    • Journal Title

      Differential and Integral equations 19

      Pages: 1047-1060

    • Related Report
      2006 Annual Research Report
  • [Journal Article] an improved remainder estimate of stationary phase method for some oscillatory integrals over a space of large dimension.2006

    • Author(s)
      Fujiwara, D., Kumanogo, N.
    • Journal Title

      Funkcialaj Ekvacioj 49/1

      Pages: 59-86

    • NAID

      130000140660

    • Related Report
      2006 Annual Research Report
  • [Journal Article] The second term of semi-classical asymptotic expansion for Feynman path integrals with integrand of polynomial growth.2006

    • Author(s)
      Fujiwara, D., Kumanogo, N.
    • Journal Title

      Journal of the Mathematical Society of Japan 58/3

      Pages: 847-867

    • NAID

      10018381149

    • Related Report
      2006 Annual Research Report
  • [Journal Article] Interface vanishing for solutions to Maxwell and Stokes systems,2006

    • Author(s)
      Kobayashi, T., Suzuki, T., Watanabe, K
    • Journal Title

      Journalof Mathematical Fluid Mechanics 8/3

      Pages: 382-397

    • Related Report
      2006 Annual Research Report
  • [Journal Article] Semiclassical singularity propagation property for Schrodinger equations

    • Author(s)
      Shu Nakamura
    • Journal Title

      Journal of the Mathematical society of Japan (to appear)

    • Related Report
      2007 Annual Research Report
    • Peer Reviewed
  • [Presentation] Remarks on scattering theory for Schr?dinger operators on scattering manifolds2010

    • Author(s)
      S. Nakamura
    • Organizer
      Spectral Problems for Quantum Hamiltonians
    • Place of Presentation
      Centre Interfacultaire Bernoulli, EPFL, Lausanne
    • Year and Date
      2010-02-22
    • Related Report
      2009 Final Research Report
  • [Presentation] Remarks on scattering theory for Schrodinger operators on scattering manifolds2010

    • Author(s)
      S.Nakamura
    • Organizer
      Spectral Problems for Quantum Hamiltonians
    • Place of Presentation
      Centre Interfacultaire Bernoulli, EPFL, Lausanne,
    • Year and Date
      2010-02-22
    • Related Report
      2009 Annual Research Report
  • [Presentation] Remarks on Fundamental Solutions to Schroedinger Equation with Variable Coefficients2010

    • Author(s)
      S. Nakamura
    • Organizer
      Spectral and Dynamical Properties of Quantum Hamiltonians
    • Place of Presentation
      Centre Interfacultaire Bernoulli, EPFL, Laussane
    • Year and Date
      2010-02-16
    • Related Report
      2009 Final Research Report
  • [Presentation] Remarks on Fundamental Solutions to Schrodinger Equation with Variable Coefficients2010

    • Author(s)
      S.Nakamura
    • Organizer
      Spectral and Dynamical Properties of Quantum Hamiltonians,
    • Place of Presentation
      Centre Interfacultaire Bernoulli, EPFL, Laussane
    • Year and Date
      2010-02-16
    • Related Report
      2009 Annual Research Report
  • [Presentation] 大次元空間上での停留位相法の剰余項評価とその経路積分への応用2010

    • Author(s)
      藤原大輔
    • Organizer
      Encounter with Mathematics
    • Place of Presentation
      中央大学理工学部
    • Year and Date
      2010-01-08
    • Related Report
      2009 Annual Research Report 2009 Final Research Report
  • [Presentation] Lifshitz tails for Schroedinger operators with non-sign definite random potentials2009

    • Author(s)
      S. Nakamura
    • Organizer
      Modeling and Understanding Random Hamiltonians: Beyond Monotonicity, Linearity and Independence
    • Place of Presentation
      Oberwolfach Mathematics Institute
    • Year and Date
      2009-12-08
    • Related Report
      2009 Final Research Report
  • [Presentation] Lifshitz tails for Schrodinger operators with non-sign definite random potentials",2009

    • Author(s)
      S.Nakamura
    • Organizer
      "Modeling and Understanding Random Hamiltonians : Beyond Monotonicity, Linearity and Independence
    • Place of Presentation
      Oberwolfach Mathematics Institute
    • Year and Date
      2009-12-08
    • Related Report
      2009 Annual Research Report
  • [Presentation] 調和振動子のある種の摂動の基本解2009

    • Author(s)
      谷島賢二
    • Organizer
      京都大学数理解析研究所研究集会「スペクトル・散乱理論とその周辺」
    • Place of Presentation
      京都大学人間環境学部
    • Year and Date
      2009-12-04
    • Related Report
      2009 Annual Research Report 2009 Final Research Report
  • [Presentation] On fundamental solution of Schroedinger equations研究集会2009

    • Author(s)
      谷島賢二
    • Organizer
      Stochastic Problems and Nonlinear PDE
    • Place of Presentation
      京都大学理学部
    • Year and Date
      2009-12-01
    • Related Report
      2009 Final Research Report
  • [Presentation] On fundamental solution of Schroedinger equations2009

    • Author(s)
      谷島賢二
    • Organizer
      研究集会[Stochastic Problems and Nonlinear PDE]
    • Place of Presentation
      京都大学理学部
    • Year and Date
      2009-12-01
    • Related Report
      2009 Annual Research Report
  • [Presentation] Remarks on scatering theory on scattering manifolds Colloque Franco-Tunisien2009

    • Author(s)
      S. Nakamura
    • Organizer
      d'equation aux derives pariellles
    • Place of Presentation
      Hammamet, Tunisia
    • Year and Date
      2009-09-28
    • Related Report
      2009 Final Research Report
  • [Presentation] Remarks on scatering theory on scattering manifolds2009

    • Author(s)
      S.Nakamura
    • Organizer
      Colloque Franco-Tunisien, dequation aux derivees pariellles,
    • Place of Presentation
      Hammamet, Tunisia,
    • Year and Date
      2009-09-28
    • Related Report
      2009 Annual Research Report
  • [Presentation] シュレーディンガー方程式の分散型評価2009

    • Author(s)
      谷島賢二
    • Organizer
      日本数学会秋季総合分科会
    • Place of Presentation
      大阪大学豊中キャンパス
    • Year and Date
      2009-09-25
    • Related Report
      2009 Final Research Report
  • [Presentation] シュレーディンガー方程式の分散型評価2009

    • Author(s)
      谷島賢二
    • Organizer
      日本数学会秋季総合分科会「秋季賞受賞講演」
    • Place of Presentation
      大阪大学豊中キャンパス
    • Year and Date
      2009-09-25
    • Related Report
      2009 Annual Research Report
  • [Presentation] シュレディンガー発展方程式の基本解について2009

    • Author(s)
      中村周
    • Place of Presentation
      大阪電気通信大学
    • Year and Date
      2009-09-21
    • Related Report
      2009 Final Research Report
  • [Presentation] 調和振動子の摂動の基本解の非有界性2009

    • Author(s)
      谷島賢二
    • Organizer
      研究集会第19回「微分方程式と数理物理」
    • Place of Presentation
      ウエルハートピア熱海(熱海)
    • Year and Date
      2009-03-16
    • Related Report
      2008 Annual Research Report
  • [Presentation] Feynman経路積分の伊藤先生による定式化について2008

    • Author(s)
      藤原大輔
    • Organizer
      伊藤清先生文化勲章祝賀講演会
    • Place of Presentation
      京都大学数理解析研究所
    • Year and Date
      2008-12-14
    • Related Report
      2009 Final Research Report
  • [Presentation] Feynman 経路積分の伊藤先生による定式化について2008

    • Author(s)
      藤原大輔
    • Organizer
      伊藤清先生文化勲章祝賀講演会
    • Place of Presentation
      京都大学数理解析研究所
    • Year and Date
      2008-12-14
    • Related Report
      2008 Annual Research Report
  • [Presentation] The second term of the semi-classical asymptotic expansion for Feynman path integrals with integrand of polynomial growth2008

    • Author(s)
      藤原大輔
    • Organizer
      Spectral Theory and Partial Differential equations
    • Place of Presentation
      Copenhagen大学
    • Year and Date
      2008-11-21
    • Related Report
      2009 Final Research Report
  • [Presentation] The second term of the semi-classical asymptotic expansion for Feynman path integrals with integrand of polynomial growth2008

    • Author(s)
      Daisuke Fujiwara
    • Place of Presentation
      Copenhagen Univ. Denmark
    • Year and Date
      2008-11-21
    • Related Report
      2008 Self-evaluation Report
  • [Presentation] The second term of the semi-classical asymptotic expansion for Feynman path integrals with integrand of polynomial growth2008

    • Author(s)
      藤原大輔
    • Organizer
      Spectral Theory and Partial Differential equations
    • Place of Presentation
      Copenhagen 大学
    • Year and Date
      2008-11-21
    • Related Report
      2008 Annual Research Report
  • [Presentation] Review of the fundamental solution to Schroedinger Equation2008

    • Author(s)
      Kenji Yajima
    • Organizer
      Mathematical Horizon of Quantum Physics
    • Place of Presentation
      Singapore国立大学
    • Year and Date
      2008-09-09
    • Related Report
      2009 Final Research Report
  • [Presentation] Revies of the fundamental solution to Schroedinger equation2008

    • Author(s)
      Kenji Yajima
    • Organizer
      Mathematical Horizon of quantum physics
    • Place of Presentation
      National Univ. Singapore, Singapore
    • Year and Date
      2008-09-09
    • Related Report
      2008 Self-evaluation Report
  • [Presentation] Review of the fundamental solution to Schroedinger Equation2008

    • Author(s)
      谷島賢二
    • Organizer
      Mathematical Horizon of Quantum Physics
    • Place of Presentation
      Singapore 国立大学(Singapore)
    • Year and Date
      2008-09-09
    • Related Report
      2008 Annual Research Report
  • [Presentation] On fundamental solution of Schroedinger equations2008

    • Author(s)
      Kenji Yajima
    • Organizer
      Meccanica, A conference in honor of S. Graffi's 65-th birthday
    • Place of Presentation
      Bologna大学
    • Year and Date
      2008-08-27
    • Related Report
      2009 Final Research Report
  • [Presentation] On fundamental solution of Schroedinger equations, Meccanica2008

    • Author(s)
      Kenji Yajima
    • Organizer
      A conference in honor of S. Graffi's 65-th birthday
    • Place of Presentation
      Univ. Bologna, Italy
    • Year and Date
      2008-08-27
    • Related Report
      2008 Self-evaluation Report
  • [Presentation] On fundamental solution of Schroedinger equations2008

    • Author(s)
      谷島賢二
    • Organizer
      Meccanica, A conference in honor of S.Graffi's 65-th birthday
    • Place of Presentation
      Bologna 大学(Italy)
    • Year and Date
      2008-08-27
    • Related Report
      2008 Annual Research Report
  • [Presentation] The L^p boundedness of wave operators for Schroedinger Operators2008

    • Author(s)
      Kenji Yajima
    • Organizer
      35-th Journees equations aux derives partielles
    • Place of Presentation
      Evian
    • Year and Date
      2008-06-03
    • Related Report
      2009 Final Research Report
  • [Presentation] The L^p boundedness of wave operators for Schroedinger operators2008

    • Author(s)
      Kenji Yajima
    • Organizer
      35-th Journees equations aux derives partielles
    • Place of Presentation
      Evian, France
    • Year and Date
      2008-06-03
    • Related Report
      2008 Self-evaluation Report
  • [Presentation] The L^p boundedness of wave operators for Schroedinger Operators2008

    • Author(s)
      谷島賢二
    • Organizer
      35-th Journees equations aux derives partielles
    • Place of Presentation
      Evian(France)
    • Year and Date
      2008-06-03
    • Related Report
      2008 Annual Research Report
  • [Presentation] Unboundedness of the fundamental solution for some perturbations of harmonic oscillators2008

    • Author(s)
      Kenji Yajima
    • Organizer
      レンヌ大学解析セミナー
    • Place of Presentation
      Rennes University
    • Year and Date
      2008-05-25
    • Related Report
      2009 Final Research Report
  • [Presentation] Unboundedness of the fundamental solution for some perturbations of harmonic oscillators2008

    • Author(s)
      谷島賢二
    • Organizer
      レンヌ大学解析セミナー
    • Place of Presentation
      Rennes University(France)
    • Year and Date
      2008-05-25
    • Related Report
      2008 Annual Research Report
  • [Presentation] Topics of Schroedinger operators, SISSA (Trieste Italy)2007

    • Author(s)
      K. Yajima
    • Organizer
      Mathematical Physics Seminar
    • Place of Presentation
      SISSA, Trieste
    • Year and Date
      2007-05-06
    • Related Report
      2009 Final Research Report
  • [Presentation] Topics of Schroedinger operators2007

    • Author(s)
      谷島 賢二
    • Organizer
      SISSA(Trieste Italy)Seminar
    • Place of Presentation
      SISSA, Trieste
    • Year and Date
      2007-05-06
    • Related Report
      2007 Annual Research Report
  • [Presentation] Lectures on topics of Schroedinger operators Lecture Series of Instituto d'Alta Matematica2007

    • Author(s)
      K. Yajima
    • Place of Presentation
      University Rome I
    • Year and Date
      2007-05-04
    • Related Report
      2009 Final Research Report
  • [Presentation] Lectures on topics of Schroedinger operators2007

    • Author(s)
      Kenji Yajima
    • Organizer
      Lecture series of Instituto d'Alta Matematica
    • Place of Presentation
      Univ. Rome I, La Sapienza, Italy
    • Year and Date
      2007-05-04
    • Related Report
      2008 Self-evaluation Report
  • [Presentation] Lectures on topics of Schroedinger operators2007

    • Author(s)
      谷島 賢二
    • Organizer
      Lecture Series of Instituto d'Alta Matematica
    • Place of Presentation
      University Rome I
    • Year and Date
      2007-05-04
    • Related Report
      2007 Annual Research Report
  • [Presentation] Existence of solution of Schroedinger operators2007

    • Author(s)
      K. Yajima
    • Organizer
      Mathematical Physics Seminar
    • Place of Presentation
      University of Bologna
    • Year and Date
      2007-04-13
    • Related Report
      2009 Final Research Report 2007 Annual Research Report
  • [Book] 応用解析ハンドブックのうち「Schroedinger方程式」の項(577から629ページ)2010

    • Author(s)
      増田久弥 編集
    • Total Pages
      629
    • Publisher
      シュプリンガー・ジャパン
    • Related Report
      2009 Annual Research Report
  • [Book] 応用解析ハンドブックのうち「Schroedinger方程式」の項2009

    • Author(s)
      谷島賢二
    • Publisher
      シュプリンガー・ジャパン
    • Related Report
      2009 Final Research Report

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Published: 2006-04-01   Modified: 2016-04-21  

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