Higuchi, Kenta Resonance free domain for a system of Schrödinger operators with energy-level crossings. (English) Zbl 07409791 Rev. Math. Phys. 33, No. 3, Article ID 2150007, 14 p. (2021). MSC: 81-XX 35P15 35C20 35S99 47A75 PDFBibTeX XMLCite \textit{K. Higuchi}, Rev. Math. Phys. 33, No. 3, Article ID 2150007, 14 p. (2021; Zbl 07409791) Full Text: DOI arXiv
Guillemin, Victor; Sternberg, Shlomo Semi-classical analysis. (English) Zbl 1298.58001 Somerville, MA: International Press (ISBN 978-1-57146-276-3/pbk). xxiv, 446 p. (2013). Reviewer: Sönke Hansen (Paderborn) MSC: 58-02 58J40 58J50 35S99 53D05 81Q20 81Q10 PDFBibTeX XMLCite \textit{V. Guillemin} and \textit{S. Sternberg}, Semi-classical analysis. Somerville, MA: International Press (2013; Zbl 1298.58001)
Dynin, Alexander Quantum energy-mass spectrum of Yang-Mills bosons. arXiv:1110.4682 Preprint, arXiv:1110.4682 [math-ph] (2011). MSC: 35S99 81T13 81T16 BibTeX Cite \textit{A. Dynin}, ``Quantum energy-mass spectrum of Yang-Mills bosons'', Preprint, arXiv:1110.4682 [math-ph] (2011) Full Text: arXiv OA License
Cordes, Heinz Otto Remarks about observables for the quantum mechanical harmonic oscillator. (English) Zbl 1189.35267 Adamyan, Vadim (ed.) et al., Modern analysis and applications. The Mark Krein centenary conference. Volume 2: Differential operators and mechanics. Papers based on invited talks at the international conference on modern analysis and applications, Odessa, Ukraine, April 9–14, 2007. Basel: Birkhäuser (ISBN 978-3-7643-9920-7/v. 2; 978-3-7643-9921-4/ebook; 978-3-7643-9924-5/set). Operator Theory: Advances and Applications 191, 305-321 (2009). Reviewer: Thierry Jecko (Cergy-Pontoise) MSC: 35Q40 35S99 81Q99 PDFBibTeX XMLCite \textit{H. O. Cordes}, Oper. Theory: Adv. Appl. 191, 305--321 (2009; Zbl 1189.35267) Full Text: DOI
Georgescu, V.; Golénia, S. Compact perturbations and stability of the essential spectrum of singular differential operators. (English) Zbl 1164.47005 J. Oper. Theory 59, No. 1, 115-155 (2008). Reviewer: Roland Duduchava (Tbilisi) MSC: 47A10 58J05 35P05 35S99 47B44 58J50 81Q10 PDFBibTeX XMLCite \textit{V. Georgescu} and \textit{S. Golénia}, J. Oper. Theory 59, No. 1, 115--155 (2008; Zbl 1164.47005)
Dorey, Patrick; Dunning, Clare; Masoero, Davide; Suzuki, Junji; Tateo, Roberto Pseudo-differential equations, and the Bethe ansatz for the classical Lie algebras. (English) Zbl 1117.35087 Nucl. Phys., B 772, No. 3, 249-289 (2007). MSC: 35S99 81T40 81Q40 81Q10 PDFBibTeX XMLCite \textit{P. Dorey} et al., Nucl. Phys., B 772, No. 3, 249--289 (2007; Zbl 1117.35087) Full Text: DOI arXiv Link
de Gosson, Maurice Symplectic geometry and quantum mechanics. (English) Zbl 1098.81004 Operator Theory: Advances and Applications 166. Advances in Partial Differential Equations. Basel: Birkhäuser (ISBN 3-7643-7574-4/hbk). xx, 367 p. (2006). Reviewer: Gheorghe Zet (Iaşi) MSC: 81-02 81S30 81Q50 53D50 53D05 35S99 34B20 47N50 81S10 PDFBibTeX XMLCite \textit{M. de Gosson}, Symplectic geometry and quantum mechanics. Basel: Birkhäuser (2006; Zbl 1098.81004)
Alexandrova, Ivana Structure of the semi-classical amplitude for general scattering relations. (English) Zbl 1088.81091 Commun. Partial Differ. Equations 30, No. 10-12, 1505-1535 (2005). Reviewer: Bogdan G. Nita (Upper Montclair) MSC: 81U05 81Q20 35P25 35S99 PDFBibTeX XMLCite \textit{I. Alexandrova}, Commun. Partial Differ. Equations 30, No. 10--12, 1505--1535 (2005; Zbl 1088.81091) Full Text: DOI arXiv
Ichinose, Takashi; Tamura, Hideo Sharp error bound on norm convergence of exponential product formula and approximation to kernels of Schrödinger semigroups. (English) Zbl 1085.47053 Commun. Partial Differ. Equations 29, No. 11-12, 1905-1918 (2004). Reviewer: Mihai Pascu (Bucureşti) MSC: 47D08 41A80 35S99 47D06 81Q15 PDFBibTeX XMLCite \textit{T. Ichinose} and \textit{H. Tamura}, Commun. Partial Differ. Equations 29, No. 11--12, 1905--1918 (2004; Zbl 1085.47053) Full Text: DOI
Sait-Ametov, M. R. Properties of 2-adic Green functions. (English) Zbl 1098.81058 Methods Funct. Anal. Topol. 10, No. 2, 69-85 (2004). Reviewer: Anatoly N. Kochubei (Kyïv) MSC: 81T08 11S85 35S99 PDFBibTeX XMLCite \textit{M. R. Sait-Ametov}, Methods Funct. Anal. Topol. 10, No. 2, 69--85 (2004; Zbl 1098.81058)
Vassilevich, Dmitri V. Noncommutative heat kernel. (English) Zbl 1053.81083 Lett. Math. Phys. 67, No. 3, 185-194 (2004). MSC: 81T75 58J35 53D55 35S99 PDFBibTeX XMLCite \textit{D. V. Vassilevich}, Lett. Math. Phys. 67, No. 3, 185--194 (2004; Zbl 1053.81083) Full Text: DOI arXiv
Georgescu, Vladimir; Golenia, Sylvain Decay Preserving Operators and Stability of the Essential Spectrum. arXiv:math/0411489 Preprint, arXiv:math/0411489 [math.SP] (2004). MSC: 47A10 58J05 35P05 35S99 47B44 58J50 81Q10 BibTeX Cite \textit{V. Georgescu} and \textit{S. Golenia}, ``Decay Preserving Operators and Stability of the Essential Spectrum'', Preprint, arXiv:math/0411489 [math.SP] (2004) Full Text: arXiv
Unterberger, André Quantization and non-holomorphic modular forms. (English) Zbl 0970.11014 Lecture Notes in Mathematics. 1742. Berlin: Springer. viii, 253 p. (2000). Reviewer: Min Ho Lee (Cedar Falls) MSC: 11F11 11-02 11F25 11L05 44A12 81S99 35-02 35S99 PDFBibTeX XMLCite \textit{A. Unterberger}, Quantization and non-holomorphic modular forms. Berlin: Springer (2000; Zbl 0970.11014) Full Text: DOI
Gielerak, R.; Ługiewicz, P. From stochastic differential equation to quantum field theory. (English) Zbl 0964.81060 Rep. Math. Phys. 44, No. 1-2, 101-110 (1999). MSC: 81T99 35S99 60H99 81S20 PDFBibTeX XMLCite \textit{R. Gielerak} and \textit{P. Ługiewicz}, Rep. Math. Phys. 44, No. 1--2, 101--110 (1999; Zbl 0964.81060) Full Text: DOI arXiv
Friedlander, Leonid; Schwarz, Albert Grassmannian and elliptic operators. (English) Zbl 0923.58053 McCleary, John (ed.), Higher homotopy structures in topology and mathematical physics. Proceedings of an international conference, June 13–15, 1996, Poughkeepsie, NY, USA, to honor the 60th birthday of Jim Stasheff. Providence, RI: American Mathematical Society. Contemp. Math. 227, 79-88 (1999). Reviewer: Vicentiu D.Rădulescu (Craiova) MSC: 58J32 35S99 81T30 PDFBibTeX XMLCite \textit{L. Friedlander} and \textit{A. Schwarz}, Contemp. Math. 227, 79--88 (1999; Zbl 0923.58053) Full Text: arXiv
Jang, Youngho An asymptotic expansion of the \(p\)-adic Green function. (English) Zbl 0917.11059 Tohoku Math. J., II. Ser. 50, No. 2, 229-242 (1998). Reviewer: Anatoly N.Kochubei (Kiev) MSC: 11S80 11Z05 81T08 81Q99 34B27 35S99 PDFBibTeX XMLCite \textit{Y. Jang}, Tôhoku Math. J. (2) 50, No. 2, 229--242 (1998; Zbl 0917.11059) Full Text: DOI
Sapuzhak, T. M. Evolution operator of a \(p\)-adic harmonic oscillator. (Ukrainian) Zbl 0936.81007 Nauk. Visn. Uzhgorod. Univ., Ser. Mat. 2, 92-101 (1997). MSC: 81Q99 81T05 11S80 47D06 35S99 PDFBibTeX XMLCite \textit{T. M. Sapuzhak}, Nauk. Visn. Uzhgorod. Univ., Ser. Mat. 2, 92--101 (1997; Zbl 0936.81007)
Kochubei, A. N. Some mathematical problems of \(p\)-adic quantum theory. (English) Zbl 0842.35147 Demuth, Michael (ed.) et al., Mathematical results in quantum mechanics: International conference in Blossin (Germany), May 17-21, 1993. Basel: Birkhäuser Verlag. Oper. Theory, Adv. Appl. 70, 353-356 (1994). MSC: 35S99 81Q99 47N50 11S80 47S10 PDFBibTeX XMLCite \textit{A. N. Kochubei}, in: Mathematical results in quantum mechanics: International conference in Blossin (Germany), May 17-21, 1993. Basel: Birkhäuser Verlag. 353--356 (1994; Zbl 0842.35147)
Kochubej, A. N. On the asymptotics of \(p\)-adic Green functions. (English. Russian original) Zbl 0904.11037 Proc. Steklov Inst. Math. 203, 105-113 (1995); translation from Tr. Mat. Inst. Steklova 203, 116-125 (1994). Reviewer: W.Wiȩsław (Wrocław) MSC: 11S80 34B27 81T08 35S99 47S10 81Q99 PDFBibTeX XMLCite \textit{A. N. Kochubej}, in: Selected questions of mathematical physics and analysis. Dedicated to the 70th anniversary of the birth of Vasilij Sergeevich Vladimirov. Providence, RI: American Mathematical Society. 1 (1994; Zbl 0904.11037); translation from Tr. Mat. Inst. Steklova 203, 116--125 (1994)
Kochubei, A. N. On \(p\)-adic Green’s functions. (English. Russian original) Zbl 0843.35147 Theor. Math. Phys. 96, No. 1, 854-865 (1993); translation from Teor. Mat. Fiz. 96, No. 1, 123-139 (1993). Reviewer: A.N.Kochubei (Kiev) MSC: 35S99 81Q99 11S80 47S10 47N50 PDFBibTeX XMLCite \textit{A. N. Kochubei}, Theor. Math. Phys. 96, No. 1, 1 (1993; Zbl 0843.35147); translation from Teor. Mat. Fiz. 96, No. 1, 123--139 (1993) Full Text: DOI
Nagase, Michihiro; Umeda, Tomio The nonrelativistic limit for the Weyl quantized Hamiltonians and pseudo- differential operators. (English) Zbl 0755.35161 Forum Math. 4, No. 4, 377-381 (1992). MSC: 35S99 47G99 81V10 PDFBibTeX XMLCite \textit{M. Nagase} and \textit{T. Umeda}, Forum Math. 4, No. 4, 377--381 (1992; Zbl 0755.35161) Full Text: DOI EuDML
Helffer, B.; Kerdelhué, P.; Sjöstrand, J. Le papillon de Hofstadter, revisité. (Hofstadter’s butterfly, revised). (French) Zbl 0732.44004 Mém. Soc. Math. Fr., Nouv. Sér. 43, 87 p. (1990). Reviewer: J.Asch (Berlin) MSC: 44A45 35Q40 35S99 35P99 81Q20 PDFBibTeX XMLCite \textit{B. Helffer} et al., Mém. Soc. Math. Fr., Nouv. Sér. 43, 87 p. (1990; Zbl 0732.44004) Full Text: Numdam EuDML
Leray, Jean The meaning of Maslov’s asymptotic method: The need of Planck’s constant in mathematics. (English) Zbl 0532.35068 The mathematical heritage of Henri Poincaré, Proc. Symp. Pure Math. 39, Part 2, Bloomington/Indiana 1980, 127-139 (1983). MSC: 35Q99 47B99 81Q99 35S99 42B99 34E20 70H03 PDFBibTeX XML
Mizrahi, Maurice M. On the WKB approximation to the propagator for arbitrary Hamiltonians. (English) Zbl 0498.70024 J. Math. Phys. 22, 102-107 (1981). MSC: 70G99 81S40 81P20 81Q05 35S99 PDFBibTeX XMLCite \textit{M. M. Mizrahi}, J. Math. Phys. 22, 102--107 (1981; Zbl 0498.70024) Full Text: DOI Link
Howe, Roger Quantum mechanics and partial differential equations. (English) Zbl 0449.35002 J. Funct. Anal. 38, 188-254 (1980). MSC: 35-02 35A99 35Q99 43A80 35S99 47B35 81Q99 PDFBibTeX XMLCite \textit{R. Howe}, J. Funct. Anal. 38, 188--254 (1980; Zbl 0449.35002) Full Text: DOI
Voros, A. Symbol calculus by symbolic computation and semi-classical expansions. (English) Zbl 0411.68038 Symbolic and algebraic computation, EUROSAM ’79, int. Symp., Marseille 1979, Lect. Notes Comput. Sci. 72, 45-51 (1979). MSC: 68W30 35J10 35S99 68Q45 34E20 41A60 81Q05 81Q15 74J99 PDFBibTeX XML
Albeverio, Sergio; Høegh-Krohn, Raphael Oscillatory integrals and the method of stationary phase in infinitely many dimensions, with applications to the classical limit of quantum mechanics. I. (English) Zbl 0449.35092 Invent. Math. 40, 59-106 (1977). MSC: 35Q99 58J99 81Q30 35S99 PDFBibTeX XMLCite \textit{S. Albeverio} and \textit{R. Høegh-Krohn}, Invent. Math. 40, 59--106 (1977; Zbl 0449.35092) Full Text: DOI