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Adiabatic Evolution and Shape Resonances
| Adiabatic Evolution and Shape Resonances |
| Autore | Hitrik Michael |
| Edizione | [1st ed.] |
| Pubbl/distr/stampa | Providence : , : American Mathematical Society, , 2022 |
| Descrizione fisica | 1 online resource (102 pages) |
| Disciplina |
515/.7242
515.7242 |
| Altri autori (Persone) |
MantileAndrea
SjöstrandJohannes |
| Collana | Memoirs of the American Mathematical Society |
| Soggetto topico |
Mathematical physics
Adiabatic invariants Partial differential equations -- Qualitative properties of solutions -- Resonances Partial differential equations -- Elliptic equations and systems -- Schrödinger operator Partial differential equations -- Spectral theory and eigenvalue problems -- Asymptotic distribution of eigenvalues and eigenfunctions Partial differential equations -- Pseudodifferential operators and other generalizations of partial differential operators -- Pseudodifferential operators |
| ISBN |
9781470472801
1470472805 |
| Classificazione | 35B3435J1035P2035S05 |
| Formato | Materiale a stampa  |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Record Nr. | UNINA-9910964406903321 |
Hitrik Michael
|
||
| Providence : , : American Mathematical Society, , 2022 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
Beyond Born-Oppenheimer [[electronic resource] ] : electronic non-adiabatic coupling terms and conical intersections / / by Michael Baer
| Beyond Born-Oppenheimer [[electronic resource] ] : electronic non-adiabatic coupling terms and conical intersections / / by Michael Baer |
| Autore | Baer M (Michael), <1937-> |
| Pubbl/distr/stampa | Hoboken, N.J., : Wiley, c2006 |
| Descrizione fisica | 1 online resource (254 p.) |
| Disciplina |
539.758
541/.28 |
| Soggetto topico |
Molecular dynamics - Mathematics
Born-Oppenheimer approximation Adiabatic invariants |
| Soggetto genere / forma | Electronic books |
| ISBN |
1-280-41143-0
9786610411436 0-470-32705-7 0-471-78008-1 0-471-78007-3 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto |
BEYOND BORN-OPPENHEIMER; CONTENTS; PREFACE; ABBREVIATIONS; 1 MATHEMATICAL INTRODUCTION; 1.1 Hilbert Space; 1.1.1 Eigenfunction and Electronic Nonadiabatic Coupling Term; 1.1.2 Abelian and Non-Abelian Curl Equations; 1.1.3 Abelian and Non-Abelian Divergence Equations; 1.2 Hilbert Subspace; 1.3 Vectorial First-Order Differential Equation and Line Integral; 1.3.1 Vectorial First-Order Differential Equation; 1.3.1.1 Study of Abelian Case; 1.3.1.2 Study of Non-Abelian Case; 1.3.1.3 Orthogonality; 1.3.2 Integral Equation; 1.3.2.1 Integral Equation along an Open Contour
1.3.2.2 Integral Equation along a Closed Contour1.3.3 Solution of Differential Vector Equation; 1.4 Summary and Conclusions; Problem; References; 2 BORN-OPPENHEIMER APPROACH: DIABATIZATION AND TOPOLOGICAL MATRIX; 2.1 Time-Independent Treatment; 2.1.1 Adiabatic Representation; 2.1.2 Diabatic Representation; 2.1.3 Adiabatic-to-Diabatic Transformation; 2.1.3.1 Transformation for Electronic Basis Sets; 2.1.3.2 Transformation for Nuclear Wavefunctions; 2.1.3.3 Implications Due to Adiabatic-to-Diabatic Transformation; 2.1.3.4 Final Comments; 2.2 Application of Complex Eigenfunctions 2.2.1 Introducing Time-Independent Phase Factors2.2.1.1 Adiabatic Schrödinger Equation; 2.2.1.2 Adiabatic-to-Diabatic Transformation; 2.2.2 Introducing Time-Dependent Phase Factors; 2.3 Time-Dependent Treatment; 2.3.1 Time-Dependent Perturbative Approach; 2.3.2 Time-Dependent Nonperturbative Approach; 2.3.2.1 Adiabatic Time-Dependent Electronic Basis Set; 2.3.2.2 Adiabatic Time-Dependent Nuclear Schrödinger Equation; 2.3.2.3 Time-Dependent Adiabatic-to-Diabatic Transformation; 2.3.3 Summary; Problem; 2A Appendixes; 2A.1 Dressed Nonadiabatic Coupling Matrix 2A.2 Analyticity of Adiabatic-to-Diabatic Transformation Matrix à in Spacetime ConfigurationReferences; 3 MODEL STUDIES; 3.1 Treatment of Analytical Models; 3.1.1 Two-State Systems; 3.1.1.1 Adiabatic-to-Diabatic Transformation Matrix; 3.1.1.2 Topological (D) Matrix; 3.1.1.3 The Diabatic Potential Matrix; 3.1.2 Three-State Systems; 3.1.2.1 Adiabatic-to-Diabatic Transformation Matrix; 3.1.2.2 Topological Matrix; 3.1.3 Four-State Systems; 3.1.3.1 Adiabatic-to-Diabatic Transformation Matrix; 3.1.3.2 Topological Matrix; 3.1.4 Comments Related to General Case 4.3 Quantization of Nonadiabatic Coupling Matrix: Study of Ab Initio Molecular Systems |
| Record Nr. | UNINA-9910143416003321 |
|
Baer M (Michael), <1937->
|
||
| Hoboken, N.J., : Wiley, c2006 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
Beyond Born-Oppenheimer [[electronic resource] ] : electronic non-adiabatic coupling terms and conical intersections / / by Michael Baer
| Beyond Born-Oppenheimer [[electronic resource] ] : electronic non-adiabatic coupling terms and conical intersections / / by Michael Baer |
| Autore | Baer M (Michael), <1937-> |
| Pubbl/distr/stampa | Hoboken, N.J., : Wiley, c2006 |
| Descrizione fisica | 1 online resource (254 p.) |
| Disciplina |
539.758
541/.28 |
| Soggetto topico |
Molecular dynamics - Mathematics
Born-Oppenheimer approximation Adiabatic invariants |
| ISBN |
1-280-41143-0
9786610411436 0-470-32705-7 0-471-78008-1 0-471-78007-3 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto |
BEYOND BORN-OPPENHEIMER; CONTENTS; PREFACE; ABBREVIATIONS; 1 MATHEMATICAL INTRODUCTION; 1.1 Hilbert Space; 1.1.1 Eigenfunction and Electronic Nonadiabatic Coupling Term; 1.1.2 Abelian and Non-Abelian Curl Equations; 1.1.3 Abelian and Non-Abelian Divergence Equations; 1.2 Hilbert Subspace; 1.3 Vectorial First-Order Differential Equation and Line Integral; 1.3.1 Vectorial First-Order Differential Equation; 1.3.1.1 Study of Abelian Case; 1.3.1.2 Study of Non-Abelian Case; 1.3.1.3 Orthogonality; 1.3.2 Integral Equation; 1.3.2.1 Integral Equation along an Open Contour
1.3.2.2 Integral Equation along a Closed Contour1.3.3 Solution of Differential Vector Equation; 1.4 Summary and Conclusions; Problem; References; 2 BORN-OPPENHEIMER APPROACH: DIABATIZATION AND TOPOLOGICAL MATRIX; 2.1 Time-Independent Treatment; 2.1.1 Adiabatic Representation; 2.1.2 Diabatic Representation; 2.1.3 Adiabatic-to-Diabatic Transformation; 2.1.3.1 Transformation for Electronic Basis Sets; 2.1.3.2 Transformation for Nuclear Wavefunctions; 2.1.3.3 Implications Due to Adiabatic-to-Diabatic Transformation; 2.1.3.4 Final Comments; 2.2 Application of Complex Eigenfunctions 2.2.1 Introducing Time-Independent Phase Factors2.2.1.1 Adiabatic Schrödinger Equation; 2.2.1.2 Adiabatic-to-Diabatic Transformation; 2.2.2 Introducing Time-Dependent Phase Factors; 2.3 Time-Dependent Treatment; 2.3.1 Time-Dependent Perturbative Approach; 2.3.2 Time-Dependent Nonperturbative Approach; 2.3.2.1 Adiabatic Time-Dependent Electronic Basis Set; 2.3.2.2 Adiabatic Time-Dependent Nuclear Schrödinger Equation; 2.3.2.3 Time-Dependent Adiabatic-to-Diabatic Transformation; 2.3.3 Summary; Problem; 2A Appendixes; 2A.1 Dressed Nonadiabatic Coupling Matrix 2A.2 Analyticity of Adiabatic-to-Diabatic Transformation Matrix à in Spacetime ConfigurationReferences; 3 MODEL STUDIES; 3.1 Treatment of Analytical Models; 3.1.1 Two-State Systems; 3.1.1.1 Adiabatic-to-Diabatic Transformation Matrix; 3.1.1.2 Topological (D) Matrix; 3.1.1.3 The Diabatic Potential Matrix; 3.1.2 Three-State Systems; 3.1.2.1 Adiabatic-to-Diabatic Transformation Matrix; 3.1.2.2 Topological Matrix; 3.1.3 Four-State Systems; 3.1.3.1 Adiabatic-to-Diabatic Transformation Matrix; 3.1.3.2 Topological Matrix; 3.1.4 Comments Related to General Case 4.3 Quantization of Nonadiabatic Coupling Matrix: Study of Ab Initio Molecular Systems |
| Record Nr. | UNINA-9910830642703321 |
|
Baer M (Michael), <1937->
|
||
| Hoboken, N.J., : Wiley, c2006 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
Beyond Born-Oppenheimer : electronic non-adiabatic coupling terms and conical intersections / / by Michael Baer
| Beyond Born-Oppenheimer : electronic non-adiabatic coupling terms and conical intersections / / by Michael Baer |
| Autore | Baer M (Michael), <1937-> |
| Pubbl/distr/stampa | Hoboken, N.J., : Wiley, c2006 |
| Descrizione fisica | 1 online resource (254 p.) |
| Disciplina | 541/.28 |
| Soggetto topico |
Molecular dynamics - Mathematics
Born-Oppenheimer approximation Adiabatic invariants |
| ISBN |
9786610411436
9781280411434 1280411430 9780470327050 0470327057 9780471780083 0471780081 9780471780076 0471780073 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto |
BEYOND BORN-OPPENHEIMER; CONTENTS; PREFACE; ABBREVIATIONS; 1 MATHEMATICAL INTRODUCTION; 1.1 Hilbert Space; 1.1.1 Eigenfunction and Electronic Nonadiabatic Coupling Term; 1.1.2 Abelian and Non-Abelian Curl Equations; 1.1.3 Abelian and Non-Abelian Divergence Equations; 1.2 Hilbert Subspace; 1.3 Vectorial First-Order Differential Equation and Line Integral; 1.3.1 Vectorial First-Order Differential Equation; 1.3.1.1 Study of Abelian Case; 1.3.1.2 Study of Non-Abelian Case; 1.3.1.3 Orthogonality; 1.3.2 Integral Equation; 1.3.2.1 Integral Equation along an Open Contour
1.3.2.2 Integral Equation along a Closed Contour1.3.3 Solution of Differential Vector Equation; 1.4 Summary and Conclusions; Problem; References; 2 BORN-OPPENHEIMER APPROACH: DIABATIZATION AND TOPOLOGICAL MATRIX; 2.1 Time-Independent Treatment; 2.1.1 Adiabatic Representation; 2.1.2 Diabatic Representation; 2.1.3 Adiabatic-to-Diabatic Transformation; 2.1.3.1 Transformation for Electronic Basis Sets; 2.1.3.2 Transformation for Nuclear Wavefunctions; 2.1.3.3 Implications Due to Adiabatic-to-Diabatic Transformation; 2.1.3.4 Final Comments; 2.2 Application of Complex Eigenfunctions 2.2.1 Introducing Time-Independent Phase Factors2.2.1.1 Adiabatic Schrödinger Equation; 2.2.1.2 Adiabatic-to-Diabatic Transformation; 2.2.2 Introducing Time-Dependent Phase Factors; 2.3 Time-Dependent Treatment; 2.3.1 Time-Dependent Perturbative Approach; 2.3.2 Time-Dependent Nonperturbative Approach; 2.3.2.1 Adiabatic Time-Dependent Electronic Basis Set; 2.3.2.2 Adiabatic Time-Dependent Nuclear Schrödinger Equation; 2.3.2.3 Time-Dependent Adiabatic-to-Diabatic Transformation; 2.3.3 Summary; Problem; 2A Appendixes; 2A.1 Dressed Nonadiabatic Coupling Matrix 2A.2 Analyticity of Adiabatic-to-Diabatic Transformation Matrix à in Spacetime ConfigurationReferences; 3 MODEL STUDIES; 3.1 Treatment of Analytical Models; 3.1.1 Two-State Systems; 3.1.1.1 Adiabatic-to-Diabatic Transformation Matrix; 3.1.1.2 Topological (D) Matrix; 3.1.1.3 The Diabatic Potential Matrix; 3.1.2 Three-State Systems; 3.1.2.1 Adiabatic-to-Diabatic Transformation Matrix; 3.1.2.2 Topological Matrix; 3.1.3 Four-State Systems; 3.1.3.1 Adiabatic-to-Diabatic Transformation Matrix; 3.1.3.2 Topological Matrix; 3.1.4 Comments Related to General Case 4.3 Quantization of Nonadiabatic Coupling Matrix: Study of Ab Initio Molecular Systems |
| Record Nr. | UNINA-9911019857903321 |
|
Baer M (Michael), <1937->
|
||
| Hoboken, N.J., : Wiley, c2006 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
The geometric phase in quantum systems : foundations, mathematical concepts, and applications in molecular and condensed matter physics / A. Bohm ... [et al.].
| The geometric phase in quantum systems : foundations, mathematical concepts, and applications in molecular and condensed matter physics / A. Bohm ... [et al.]. |
| Pubbl/distr/stampa | Berlin : Springer, c2003 |
| Descrizione fisica | xv, 439 p. : ill. ; 24 cm |
| Disciplina | 530.12 |
| Altri autori (Persone) | Bohm, Arno |
| Collana | Texts and monographs in physics, 0172-5998 |
| Soggetto topico |
Geometric quantum phases
Adiabatic invariants Quantum theory |
| ISBN | 3540000313 |
| Classificazione |
AMS 81Q70
AMS 81-02 LC QC20.7.G44G457 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Record Nr. | UNISALENTO-991003329039707536 |
| Berlin : Springer, c2003 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. del Salento | ||
| ||
