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Quantum Oscillators [Hardback]

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  • Formāts: Hardback, 672 pages, height x width x depth: 243x161x39 mm, weight: 1139 g
  • Izdošanas datums: 15-Jul-2011
  • Izdevniecība: John Wiley & Sons Inc
  • ISBN-10: 047046609X
  • ISBN-13: 9780470466094
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Quantum OscillatorsPalielināt
  • Formāts: Hardback, 672 pages, height x width x depth: 243x161x39 mm, weight: 1139 g
  • Izdošanas datums: 15-Jul-2011
  • Izdevniecība: John Wiley & Sons Inc
  • ISBN-10: 047046609X
  • ISBN-13: 9780470466094
Citas grāmatas par šo tēmu:
Permanent link: https://www.kriso.lv/db/9780470466094.html
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"Quantum Oscillators is a valuable source of information and an excellent supplementary text in courses on spectroscopy of hydrogen-bonded systems, one of the unsolved problems of science. This reference provides a reasonable and accessible entrance to the difficult subject of nonequilibrium quantum mechanics and is a timely update of classical works while, at the same time, providing a comprehensive treatment of hydrogen bonding. Also included is an appendix that summarizes mathematical concepts needed to understand the basis of the theory"--

"The book is divided into four parts. The first part is devoted to the concepts of quantum mechanics the knowledge of which is necessary for a good understanding of the dynamics of quantum oscillator which may be damped, and deals with time independent quantum mechanics and time dependent quantum mechanics"--

Provided by publisher.

Quantum Oscillators  is a valuable source of information and an excellent supplementary text in courses on spectroscopy of hydrogen-bonded systems, one of the unsolved problems of science. This reference provides a reasonable and accessible entrance to the difficult subject of nonequilibrium quantum mechanics and is a timely update of classical works while, at the same time, providing a comprehensive treatment of hydrogen bonding. Also included is an appendix that summarizes mathematical concepts needed to understand the basis of the theory.
List of Figures
xiii
Preface xvii
Acknowledgments xxiii
PART I BASIS REQUIRED FOR QUANTUM OSCILLATOR STUDIES
Chapter 1 Basic Concepts Required For Quantum Mechanics
1.1 Basic Concepts of Complex Vectorial Spaces
3(5)
1.2 Hermitian Conjugation
8(4)
1.3 Hermiticity and Unitarity
12(6)
1.4 Algebra Operators
18(3)
Chapter 2 Basis For Quantum Approaches Of Oscillators
2.1 Oscillator Quantization at the Historical Origin of Quantum Mechanics
21(4)
2.2 Quantum Mechanics Postulates and Noncommutativity
25(5)
2.3 Heisenberg Uncertainty Relations
30(7)
2.4 Schrodinger Picture Dynamics
37(8)
2.5 Position or Momentum Translation Operators
45(9)
2.6 Conclusion
54(3)
Bibliography
55(2)
Chapter 3 Quantum Mechanics Representations
3.1 Matrix Representation
57(11)
3.2 Wave Mechanics
68(8)
3.3 Evolution Operators
76(12)
3.4 Density operators
88(16)
3.5 Conclusion
104(3)
Bibliography
106(1)
Chapter 4 Simple Models Useful For Quantum Oscillator Physics
4.1 Particle-in-a-Box Model
107(8)
4.2 Two-Energy-Level Systems
115(13)
4.3 Conclusion
128(3)
Bibliography
128(3)
PART II SINGLE QUANTUM HARMONIC OSCILLATORS
Chapter 5 Energy Representation For Quantum Harmonic Oscillator
5.1 Hamiltonian Eigenkets and Eigenvalues
131(19)
5.2 Wavefunctions Corresponding to Hamiltonian Eigenkets
150(6)
5.3 Dynamics
156(6)
5.4 Boson and fermion operators
162(3)
5.5 Conclusion
165(3)
Bibliography
166(2)
Chapter 6 Coherent States And Translation Operators
6.1 Coherent-State Properties
168(6)
6.2 Poisson Density Operator
174(1)
6.3 Average and Fluctuation of Energy
175(2)
6.4 Coherent States as Minimizing Heisenberg Uncertainty Relations
177(3)
6.5 Dynamics
180(3)
6.6 Translation Operators
183(3)
6.7 Coherent-State Wavefunctions
186(3)
6.8 Franck-Condon Factors
189(4)
6.9 Driven Harmonic Oscillators
193(4)
6.10 Conclusion
197(2)
Bibliography
198(1)
Chapter 7 Boson Operator Theorems
7.1 Canonical Transformations
199(5)
7.2 Normal and Antinormal Ordering Formalism
204(13)
7.3 Time Evolution Operator of Driven Harmonic Oscillators
217(4)
7.4 Conclusion
221(2)
Bibliography
222(1)
Chapter 8 Phase Operators And Squeezed States
8.1 Phase Operators
223(6)
8.2 Squeezed States
229(10)
8.3 Bogoliubov-Valatin transformation
239(2)
8.4 Conclusion
241(4)
Bibliography
241(4)
PART III ANHARMONICITY
Chapter 9 Anharmonic Oscillators
9.1 Model for Diatomic Molecule Potentials
245(6)
9.2 Harmonic oscillator perturbed by a Q3 potential
251(6)
9.3 Morse Oscillator
257(8)
9.4 Quadratic Potentials Perturbed by Cosine Functions
265(2)
9.5 Double-well potential and tunneling effect
267(10)
9.6 Conclusion
277(2)
Bibliography
277(2)
Chapter 10 Oscillators Involving Anharmonic Couplings
10.1 Fermi resonances
279(3)
10.2 Strong Anharmonic Coupling Theory
282(3)
10.3 Strong Anharmonic Coupling within the Adiabatic Approximation
285(12)
10.4 Fermi Resonances and Strong Anharmonic Coupling within Adiabatic Approximation
297(4)
10.5 Davydov and Strong Anharmonic Couplings
301(11)
10.6 Conclusion
312(5)
Bibliography
312(5)
PART IV OSCILLATOR POPULATIONS IN THERMAL EQUILIBRIUM
Chapter 11 Dynamics Of A Large Set Of Coupled Oscillators
11.1 Dynamical Equations in the Normal Ordering Formalism
317(6)
11.2 Solving the linear set of differential equations (11.27)
323(2)
11.3 Obtainment of the Dynamics
325(4)
11.4 Application to a Linear Chain
329(2)
11.5 Conclusion
331(2)
Bibliography
331(2)
Chapter 12 Density Operators For Equilibrium Populations Of Oscillators
12.1 Boltzmann's H-Theorem
333(4)
12.2 Evolution Toward Equilibrium of a Large Population of Weakly Coupled Harmonic Oscillators
337(11)
12.3 Microcanonical Systems
348(1)
12.4 Equilibrium Density Operators from Entropy Maximization
349(9)
12.5 Conclusion
358(3)
Bibliography
359(2)
Chapter 13 Thermal Properties Of Harmonic Oscillators
13.1 Boltzmann Distribution Law inside a Large Population of Equivalent Oscillators
361(3)
13.2 Thermal properties of harmonic oscillators
364(24)
13.3 Helmholtz Potential for Anharmonic Oscillators
388(3)
13.4 Thermal Average of Boson Operator Functions
391(12)
13.5 Conclusion
403(6)
Bibliography
405(4)
PART V QUANTUM NORMAL MODES OF VIBRATION
Chapter 14 Quantum Electromagnetic Modes
14.1 Maxwell Equations
409(6)
14.2 Electromagnetic Field Hamiltonian
415(3)
14.3 Polarized Normal Modes
418(2)
14.4 Normal Modes of a Cavity
420(3)
14.5 Quantization of the Electromagnetic Fields
423(14)
14.6 Some Thermal Properties of the Quantum Fields
437(5)
14.7 Conclusion
442(1)
Bibliography
442(1)
Chapter 15 Quantum Modes In Molecules And Solids
15.1 Molecular Normal Modes
443(8)
15.2 Phonons and Normal Modes in Solids
451(9)
15.3 Einstein and Debye Models of Heat Capacity
460(4)
15.4 Conclusion
464(4)
Bibliography
464(4)
PART VI DAMPED HARMONIC OSCILLATORS
Chapter 16 Damped Oscillators
16.1 Quantum Model for Damped Harmonic Oscillators
468(7)
16.2 Second-Order Solution of Eq. (16.41)
475(19)
16.3 Fokker-Planck Equation Corresponding to (16.114)
494(4)
16.4 Nonperturbative Results for Density Operator
498(5)
16.5 Langevin Equations for Ladder Operators
503(6)
16.6 Evolution Operators of Driven Damped Oscillators
509(6)
16.7 Conclusion
515(4)
Bibliography
516(3)
PART VII VIBRATIONAL SPECTROSCOPY
Chapter 17 Applications To Oscillator Spectroscopy
17.1 IR Selection Rules for Molecular Oscillators
519(15)
17.2 IR Spectra within the Linear Response Theory
534(5)
17.3 IR Spectra of Weak H-Bonded Species
539(9)
17.4 SD of Damped Weak H-Bonded Species
548(2)
17.5 Approximation for Quantum Damping
550(5)
17.6 Damped Fermi Resonances
555(6)
17.7 H-Bonded IR Line Shapes Involving Fermi Resonance
561(5)
17.8 Line Shapes of H-Bonded Cyclic Dimers
566(21)
Bibliography
584(3)
Chapter 18 Appendix
18.1 An Important Commutator
587(1)
18.2 An Important Basic Canonical Transformation
587(2)
18.3 Canonical Transformation on a Function of Operators
589(1)
18.4 Glauber-Weyl Theorem
590(1)
18.5 Commutators of Functions of the P and Q operators
591(2)
18.6 Distribution Functions and Fourier Transforms
593(11)
18.7 Lagrange Multipliers Method
604(1)
18.8 Triple Vector Product
605(2)
18.9 Point Groups
607(15)
18.10 Scientific Authors Appearing in the Book
622(13)
Index 635
Olivier Henri-Rousseau, Emeritus Professor in Theoretical Chemistry at the University of the Perpignan in France, was the founder of the Laboratory of Mathematics and Physics at the university. After proposing an explanation of the regioselectivity of 1-3 dipolar cycloadditions (simultaneously with Professor Kendall N. Houk), he worked in the area of the quantum theory of hydrogen bonding IR spectroscopy. He has penned eighty-four papers, contributed chapters to eleven books, and recently wrote a book on the epistemology of Darwinism.

Paul Blaise, Full Professor in Chemical Physics at the University of Perpignan in France, works with Professor Henri-Rousseau in the areas of chemical physics, quantum chemistry and chemical education. He belongs to the Laboratory of Mathematics and Physics and has published fifty-seven articles and six book chapters.