Time Dependent Quantum Mechanics and Spectroscopy

by Andrei Tokmakoff

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These notes are meant as a resource for chemists that study the time-dependent quantum mechanics, dynamics, and spectroscopy of molecular systems.

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Publisher
University of Chicago
Subjects
Chemistry, Physical and Theoretical Chemistry Textbook Maps
Licence
CC BY-NC-SA 4.0, as LibreTexts states it. Non-commercial use only.
Who can read
Tweens profiles and older, judged from its title and subjects

Contents

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  1. Front Matter
  2. TitlePage
  3. InfoPage
  4. Table of Contents
  5. Licensing
  6. 1: Overview of Time-Independent Quantum Mechanics
  7. 1.1: Describing a System Quantum Mechanically
  8. 1.2: Matrix Mechanics
  9. 1.3: Basic Quantum Mechanical Models
  10. 1.4: Exponential Operators
  11. 1.5: Numerically Solving the Schrödinger Equation
  12. 2: Introduction to Time-Dependent Quantum Mechanics
  13. 2.1: Time-Evolution with a Time-Independent Hamiltonian
  14. 2.2: Exponential Operators Again
  15. 2.3: Two-Level Systems
  16. 3: Time-Evolution Operator
  17. 3.1: Time-Evolution Operator
  18. 3.2: Integrating the Schrödinger Equation Directly
  19. 3.3: Transitions Induced by Time-Dependent Potential
  20. 3.4: Resonant Driving of a Two-Level System
  21. 3.5: Schrödinger and Heisenberg Representations
  22. 3.6: Interaction Picture
  23. 3.7: Time-Dependent Perturbation Theory
  24. 3.8: Fermi’s Golden Rule
  25. 4: Irreversible Relaxation
  26. 4.1: Introduction to Dissipative Dynamics
  27. 5: The Density Matrix
  28. 5.1: Introduction to the Density Matrix
  29. 5.2: Time-Evolution of the Density Matrix
  30. 5.3: The Density Matrix in the Interaction Picture
  31. 6: Adiabatic Approximation
  32. 6.1: Born–Oppenheimer Approximation
  33. 6.2: Nonadiabatic Effects
  34. 6.3: Diabatic and Adiabatic States
  35. 6.4: Adiabatic and Nonadiabatic Dynamics
  36. 6.5: Landau–Zener Transition Probability
  37. 7: Interaction of Light and Matter
  38. 7.1: Introduction to Light-Matter Interactions
  39. 7.2: Classical Light–Matter Interactions
  40. 7.3: Quantum Mechanical Electric Dipole Hamiltonian
  41. 7.4: Relaxation and Line-Broadening
  42. 7.5: Absorption Cross-Sections
  43. 7.6: Appendix - Review of Free Electromagnetic Field
  44. 7.7: Appendix - Magnetic Dipole and Electric Quadrupole Transitions
  45. 8: Mixed States and the Density Matrix
  46. 8.1: Mixed States
  47. 8.2: Density Matrix for a Mixed State
  48. 9: Irreversible and Random Processes
  49. 9.1: Concepts and Definitions
  50. 9.2: Thermal Equilibrium
  51. 9.3: Fluctuations
  52. 10: Time-Correlation Functions
  53. 10.1: Definitions, Properties, and Examples of Correlation Functions
  54. 10.2: Correlation Function from a Discrete Trajectory
  55. 10.3: Quantum Time-Correlation Functions
  56. 10.4: Transition Rates from Correlation Functions
  57. 11: Linear Response Theory
  58. 11.1: Classical Linear Response Theory
  59. 11.2: Quantum Linear Response Functions
  60. 11.3: The Response Function and Energy Absorption
  61. 11.4: Relaxation of a Prepared State
  62. 12: Time-domain Description of Spectroscopy
  63. 12.1: A Classical Description of Spectroscopy
  64. 12.2: Time-Correlation Function Description of Absorption Lineshape
  65. 12.3: Different Types of Spectroscopy Emerge from the Dipole Operator
  66. 12.4: Ensemble Averaging and Line-Broadening
  67. 13: Coupling of Electronic and Nuclear Motion
  68. 13.1: The Displaced Harmonic Oscillator Model
  69. 13.2: Coupling to a Harmonic Bath
  70. 13.3: Semiclassical Approximation to the Dipole Correlation Function
  71. 14: Fluctuations in Spectroscopy
  72. 14.1: Fluctuations and Randomness - Some Definitions
  73. 14.2: Line-Broadening and Spectral Diffusion
  74. 14.3: Gaussian-Stochastic Model for Spectral Diffusion
  75. 14.4: The Energy Gap Hamiltonian
  76. 14.5: Correspondence of Harmonic Bath and Stochastic Equations of Motion
  77. 15: Energy and Charge Transfer
  78. 15.1: Electronic Interactions
  79. 15.2: Förster Resonance Energy Transfer (FRET)
  80. 15.3: Excitons in Molecular Aggregates
  81. 15.4: Multiple Particles and Second Quantization
  82. 15.5: Marcus Theory for Electron Transfer
  83. 16: Quantum Relaxation Processes
  84. 16.1: Vibrational Relaxation
  85. 16.2: A Density Matrix Description of Quantum Relaxation
  86. Back Matter
  87. Index
  88. Glossary
  89. Detailed Licensing