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Volumn 223, Issue 3, 2001, Pages 583-626

A time-dependent Born-Oppenheimer approximation with exponentially small error estimates

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EID: 0035540307     PISSN: 00103616     EISSN: None     Source Type: Journal    
DOI: 10.1007/s002200100562     Document Type: Article
Times cited : (50)

References (33)
  • 1
    • 0000697533 scopus 로고    scopus 로고
    • Estimations de diffusion pour un opérateur de Klein-Gordon matriciel dépendant du temps
    • 1. Benchaou, M.: Estimations de Diffusion pour un Opérateur de Klein-Gordon Matriciel Dépendant du Temps. Bull. Soc. math. France 126, 273-294 (1998)
    • (1998) Bull. Soc. Math. France , vol.126 , pp. 273-294
    • Benchaou, M.1
  • 2
    • 0001671091 scopus 로고    scopus 로고
    • Estimations exponentielles en théorie de la diffusion des opérateurs de Schrödinger matriciels
    • 2. Benchaou, M., and Martinez A.: Estimations Exponentielles en Théorie de la Diffusion des Opérateurs de Schrödinger Matriciels. Ann. Inst. H. Poincaré Sect. A 71, 561-594 (1999)
    • (1999) Ann. Inst. H. Poincaré Sect. A , vol.71 , pp. 561-594
    • Benchaou, M.1    Martinez, A.2
  • 3
    • 0003147236 scopus 로고
    • Quantum phase corrections from adiabatic iteration
    • 3. Berry, M.V.: Quantum Phase Corrections from Adiabatic Iteration. Proc. R. Soc. Lond. A 414, 31-46 (1987)
    • (1987) Proc. R. Soc. Lond. A , vol.414 , pp. 31-46
    • Berry, M.V.1
  • 4
    • 0002238196 scopus 로고
    • Histories of adiabatic quantum transitions
    • 4. Berry, M.V.: Histories of Adiabatic Quantum Transitions. Proc. R. Soc. Lond. A 429, 61-72 (1990)
    • (1990) Proc. R. Soc. Lond. A , vol.429 , pp. 61-72
    • Berry, M.V.1
  • 5
    • 36449001803 scopus 로고
    • Methods for molecular-dynamics with nonadiabtic transitions
    • 5. Coker, D. F., and Xiao, L: Methods for Molecular-Dynamics with Nonadiabtic Transitions. J. Chem. Phys. 102, 496-510 (1995)
    • (1995) J. Chem. Phys. , vol.102 , pp. 496-510
    • Coker, D.F.1    Xiao, L.2
  • 7
    • 0002241894 scopus 로고
    • A time-dependent Born-Oppenheimer approximation
    • 7. Hagedorn, G. A.: A Time-Dependent Born-Oppenheimer Approximation. Commun. Math. Phys. 77, 1-19 (1980)
    • (1980) Commun. Math. Phys. , vol.77 , pp. 1-19
    • Hagedorn, G.A.1
  • 8
    • 0001451057 scopus 로고
    • High order corrections to the time-dependent Born-Oppenheimer approximation I: Smooth potentials
    • Erratum 126, 219 (1987)
    • 8. Hagedorn, G. A.: High Order Corrections to the Time-Dependent Born-Oppenheimer Approximation I: Smooth Potentials. Ann. Math. 124, 571-590 (1986). Erratum 126, 219 (1987)
    • (1986) Ann. Math. , vol.124 , pp. 571-590
    • Hagedorn, G.A.1
  • 9
    • 0007159151 scopus 로고
    • High order corrections to the time-dependent Born-Oppenheimer approximation II: Coulomb systems
    • 9. Hagedorn, G. A.: High Order Corrections to the Time-Dependent Born-Oppenheimer Approximation II: Coulomb Systems. Commun. Math. Phys. 117, 387-403 (1988)
    • (1988) Commun. Math. Phys. , vol.117 , pp. 387-403
    • Hagedorn, G.A.1
  • 10
    • 0001118605 scopus 로고
    • Molecular propagation through electronic eigenvalue crossings
    • 10. Hagedorn, G. A.: Molecular Propagation Through Electronic Eigenvalue Crossings, Memoirs Amer. Math. Soc. 111 (536), (1994)
    • (1994) Memoirs Amer. Math. Soc. , vol.111 , pp. 536
    • Hagedorn, G.A.1
  • 11
    • 34047190051 scopus 로고
    • Semiclassical quantum mechanics III: The large order asymptotics and more general states
    • 11. Hagedorn, G. A.: Semiclassical Quantum Mechanics III: The Large Order Asymptotics and More General States. Ann. Phys. 135, 58-70 (1981)
    • (1981) Ann. Phys. , vol.135 , pp. 58-70
    • Hagedorn, G.A.1
  • 12
    • 0003219943 scopus 로고
    • Semiclassical quantum mechanics IV: Large order asymptotics and more general states in more than one dimension
    • 12. Hagedorn, G. A.: Semiclassical Quantum Mechanics IV: Large Order Asymptotics and More General States in More than One Dimension. Ann. Inst. H. Poincaré Sect. A. 42, 363-374 (1985)
    • (1985) Ann. Inst. H. Poincaré Sect. A , vol.42 , pp. 363-374
    • Hagedorn, G.A.1
  • 13
    • 0002297877 scopus 로고    scopus 로고
    • Raising and lowering operators for semiclassical wave packets
    • 13. Hagedorn, G. A.: Raising and lowering operators for semiclassical wave packets. Ann. Phys. 269, 77-104 (1998)
    • (1998) Ann. Phys. , vol.269 , pp. 77-104
    • Hagedorn, G.A.1
  • 14
    • 0033517595 scopus 로고    scopus 로고
    • Semiclassical dynamics with exponentially small error estimates
    • 14. Hagedorn, G. A. and Joye, A.: Semiclassical Dynamics with Exponentially Small Error Estimates. Commun. Math. Phys. 207, 439-465 (1999)
    • (1999) Commun. Math. Phys. , vol.207 , pp. 439-465
    • Hagedorn, G.A.1    Joye, A.2
  • 15
    • 0034346372 scopus 로고    scopus 로고
    • Exponentially accurate semiclassical dynamics: Propagation, localization, ehrenfest times, scattering and more general states
    • 15. Hagedorn, G. A., and Joye, A.: Exponentially Accurate Semiclassical Dynamics: Propagation, Localization, Ehrenfest Times, Scattering and More General States. Ann. H. Poincaré 1, 837-883 (2000)
    • (2000) Ann. H. Poincaré , vol.1 , pp. 837-883
    • Hagedorn, G.A.1    Joye, A.2
  • 16
    • 0028495271 scopus 로고
    • Proof of the Landau-Zener formula
    • 16. Joye, A.: Proof of the Landau-Zener Formula. Asymptotic Analysis 9, 209-258 (1994)
    • (1994) Asymptotic Analysis , vol.9 , pp. 209-258
    • Joye, A.1
  • 17
    • 0003122119 scopus 로고
    • Exponentially small adiabatic invariant for the Schrödinger equation
    • 17. Joye, A. and Pfister, C.-E.: Exponentially Small Adiabatic Invariant for the Schrödinger Equation. Commun. Math. Phys. 140, 15-41 (1991)
    • (1991) Commun. Math. Phys. , vol.140 , pp. 15-41
    • Joye, A.1    Pfister, C.-E.2
  • 18
    • 21144476366 scopus 로고
    • Superadiabatic evolution and adiabatic transition probability between two non-degenerate levels isolated in the spectrum
    • 18. Joye, A. and Pfister, C.-E.: Superadiabatic Evolution and Adiabatic Transition Probability between Two Non-Degenerate Levels Isolated in the Spectrum. J. Math. Phys. 34, 454-479 (1993)
    • (1993) J. Math. Phys. , vol.34 , pp. 454-479
    • Joye, A.1    Pfister, C.-E.2
  • 19
    • 0042525953 scopus 로고
    • Semi-classical asymptotics beyond all Orders for simple scattering systems
    • 19. Joye, A., Pfister, C.-E. : Semi-Classical Asymptotics beyond All Orders for Simple Scattering Systems, SIAM J. Math. Anal. 26, 944-977 (1995)
    • (1995) SIAM J. Math. Anal. , vol.26 , pp. 944-977
    • Joye, A.1    Pfister, C.-E.2
  • 20
    • 0007156294 scopus 로고
    • On the mathematical theory of predissociation
    • 20. Klein, M.: On the Mathematical Theory of Predissociation. Ann. Phys. 178, 48-73 (1987)
    • (1987) Ann. Phys. , vol.178 , pp. 48-73
    • Klein, M.1
  • 21
    • 36149037026 scopus 로고
    • Superadiabatic tracking of quantum evolution
    • 21. Lim R., and Berry, M.V.: Superadiabatic Tracking of Quantum Evolution. J. Phys. A: Math. Gen. 24, 3255-3264 (1991)
    • (1991) J. Phys. A: Math. Gen. , vol.24 , pp. 3255-3264
    • Lim, R.1    Berry, M.V.2
  • 22
    • 0001666441 scopus 로고
    • Semiclassical inelastic S-Matrix for one-dimensional N-states systems
    • 22. Martin Ph.-A. and Nenciu G.: Semiclassical Inelastic S-Matrix for One-Dimensional N-States Systems, Rev. Math. Phys. 7, 193-242 (1995)
    • (1995) Rev. Math. Phys. , vol.7 , pp. 193-242
    • Martin, Ph.-A.1    Nenciu, G.2
  • 23
    • 0004081829 scopus 로고
    • Développements asymptotiques et effet tunnel dans l'approximation de Born-Oppenheimer
    • 23. Martinez, A.: Développements Asymptotiques et Effet Tunnel dans l'Approximation de Born-Oppenheimer. Ann. Inst. H. Poincaré Sect. A 50, 239-257 (1989)
    • (1989) Ann. Inst. H. Poincaré Sect. A , vol.50 , pp. 239-257
    • Martinez, A.1
  • 24
    • 0001756368 scopus 로고
    • Resonances dans l'approximation de Born-Oppenheimer I
    • 24. Martinez, A.: Resonances dans l'Approximation de Born-Oppenheimer I. J. Diff. Eq. 91, 204-234 (1991)
    • (1991) J. Diff. Eq. , vol.91 , pp. 204-234
    • Martinez, A.1
  • 25
    • 0007157572 scopus 로고
    • Resonances dans l'approximation de Born-Oppenheimer II. Largeur de résonances
    • 25. Martinez, A.: Resonances dans l'Approximation de Born-Oppenheimer II. Largeur de Résonances. Commun. Math. Phys. 135, 517-530 (1991)
    • (1991) Commun. Math. Phys. , vol.135 , pp. 517-530
    • Martinez, A.1
  • 27
    • 0007286918 scopus 로고
    • Linear adiabatic theory and applications: Exponential estimates
    • 27. Nenciu, G.: Linear Adiabatic Theory and Applications: Exponential Estimates. Commun. Math. Phys. 152, 121-135 (1993)
    • (1993) Commun. Math. Phys. , vol.152 , pp. 121-135
    • Nenciu, G.1
  • 29
    • 36049058509 scopus 로고
    • Time-dependent semiclassical scattering theory. II. Atomic collisions
    • 29. Pechukas, P.: Time-Dependent Semiclassical Scattering Theory. II. Atomic Collisions. Phys. Rev. 181, 174-184 (1969)
    • (1969) Phys. Rev. , vol.181 , pp. 174-184
    • Pechukas, P.1
  • 32
    • 13044304431 scopus 로고
    • Molecular dynamics with electronic transitions
    • 32. Tully, J. C.: Molecular Dynamics with Electronic Transitions. J. Chem. Phys. 93, 1061-1071 (1990)
    • (1990) J. Chem. Phys. , vol.93 , pp. 1061-1071
    • Tully, J.C.1
  • 33
    • 0026103656 scopus 로고
    • Nonadiabatic processes in condensed matter: Semi-classical theory and implementation
    • 33. Webster, F., Rossky, P. J., and Friesner, R. A.: Nonadiabatic Processes in Condensed Matter: Semi-Classical Theory and Implementation. Comp. Phys. Commun. 63, 494-522 (1991)
    • (1991) Comp. Phys. Commun. , vol.63 , pp. 494-522
    • Webster, F.1    Rossky, P.J.2    Friesner, R.A.3


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.