Time Dependent Quantum Mechanics and Spectroscopy 2025e

by Andrei Tokmakoff

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This book is meant as a resource for those that study quantum mechanics, dynamics, and spectroscopy of molecular systems. It's written with chemists in mind: people whose view of the world is formed in the language of atoms and molecules. It is also meant as a reference for practitioners in the field who may be familiar with the topic but perhaps not the molecular perspective. This edition adds considerable new material to the 2014 edition as well as extensive editing to the whole book.

Description from LibreTexts.

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. Title Page
  3. Info Page
  4. Table of Contents
  5. Licensing
  6. Preface
  7. 1: Overview of Time-Independent Quantum Mechanics
  8. 1.1: Introduction
  9. 1.2: Describing a System Quantum Mechanically
  10. 1.3: Dirac Notation and Matrix Mechanics
  11. 1.4: Basic Quantum Models
  12. 1.5: Raising and Lowering Operators
  13. 1.6: Angular Momentum
  14. 1.7: Exponential Operators
  15. 1.8: Readings
  16. 2: The Schrödinger Equation and Time-Propagator
  17. 2.1: Dynamics with a Time-Independent Hamiltonian
  18. 2.2: Time-Evolution Operator
  19. 2.3: Two-Level System
  20. 2.4: Equation of Motion for the Time-Evolution Operator
  21. 2.5: Dynamics with a Time-Dependent Hamiltonian
  22. 2.6: Schrödinger and Heisenberg Representations
  23. 2.7: Readings
  24. 3: Solving the Time-Dependent Schrödinger Equation
  25. 3.1: Introduction
  26. 3.2: Integrating the TDSE Directly
  27. 3.3: Transitions Induced by a Time-Dependent Potential
  28. 3.4: Resonant Driving of a Two-Level System
  29. 3.5: The Interaction Picture
  30. 3.6: Time-Dependent Perturbation Theory
  31. 3.7: The Golden Rule
  32. 3.8: Readings
  33. 4: Wavepacket Dynamics
  34. 4.1: Position and Momentum Representation
  35. 4.2: Free-Particle Eigenstates
  36. 4.3: Free-Particle Wavepacket
  37. 4.4: Readings
  38. 5: Adiabatic Approximation
  39. 5.1: Adiabatic Processes
  40. 5.2: Born–Oppenheimer Approximation
  41. 5.3: Nonadiabatic Coupling
  42. 5.4: Diabatic and Adiabatic States
  43. 5.5: Landau–Zener Transition Probability
  44. 5.6: Adiabaticity criterion
  45. 5.7: Readings
  46. 6: Classical Description of Spectroscopy
  47. 6.1: Introduction
  48. 6.2: Absorption by a Driven Oscillator
  49. 6.3: Complex formulation of the driven dipole oscillator
  50. 6.4: Response of an Impulsively Driven Oscillator
  51. 6.5: Polarizability
  52. 6.6: Appendix- Laplace Transform Solution for the Driven Damped Oscillator
  53. 6.7: Readings
  54. 7: Interaction of Light and Matter
  55. 7.1: Introduction
  56. 7.2: Electromagnetic Plane Waves
  57. 7.3: Classical Light–Matter Interactions
  58. 7.4: Electric Dipole Hamiltonian
  59. 7.5: The Dipole Operator and Transition Dipole Matrix Elements
  60. 7.6: Absorption Cross Section
  61. 7.7: Quantitative Examples of Light-Matter Interactions
  62. 7.8: Appendix- Electromagnetic Fields and Potentials
  63. 7.9: Appendix- Magnetic Dipole and Electric Quadrupole Transitions
  64. 7.10: Readings
  65. 8: Emission of Radiation
  66. 8.1: Classical rate of light emission
  67. 8.2: Radiation from an Oscillating Dipole
  68. 8.3: Appendix- Wave equation with a source
  69. 8.4: Readings
  70. 9: Quantum Electromagnetic Field
  71. 9.1: Introduction
  72. 9.2: Hamiltonian for quantized electromagnetic field
  73. 9.3: Electromagnetic field
  74. 9.4: Light-Matter Interactions and Spontaneous Emission
  75. 9.5: Coherent States
  76. 9.6: Readings
  77. 10: Transition Dipole Moment and Selection Rules
  78. 10.1: The Molecular Transition Dipole Moment
  79. 10.2: Selection Rules in the Electric Dipole Approximation
  80. 10.3: Molecular Electronic Spectroscopy and Franck Condon Factors
  81. 10.4: Appendix - Rotational Transition Matrix Elements
  82. 10.5: Readings
  83. 11: Irreversible Relaxation
  84. 11.1: Introduction
  85. 11.2: Coupling to a continuum
  86. 11.3: Spontaneous Emission
  87. 11.4: Relaxation and Line-broadening
  88. 11.5: Readings
  89. 12: Quantum Statistical Mechanics For Condensed Matter
  90. 12.1: Concepts for Condensed Matter
  91. 12.2: Statistics of Ensembles
  92. 12.3: Equilibrium Systems
  93. 12.4: Mixed States
  94. 12.5: The Density Matrix
  95. 12.6: Time-Dependence of the Density Matrix
  96. 12.7: Readings
  97. 13: Correlation Functions
  98. 13.1: Classical Time-Correlation Functions
  99. 13.2: Examples of Classical Time-Correlation Functions
  100. 13.3: Calculating the Correlation Function from a Discrete Trajectory
  101. 13.4: Quantum Time-Correlation Functions
  102. 13.5: Transition Rates from Time Correlation Functions
  103. 13.6: Appendix- Weiner-Khinchin Theorem and the Power Spectrum
  104. 13.7: Readings
  105. 14: Linear Response Theory
  106. 14.1: Classical Linear Response Theory
  107. 14.2: Example- Response of a damped harmonic oscillator
  108. 14.3: The Response Function and Energy Absorption
  109. 14.4: Quantum Linear Response Functions
  110. 14.5: Nonlinear response functions
  111. 14.6: Relaxation of a Prepared State
  112. 14.7: Example- Response of an abruptly shifted oscillator
  113. 14.8: Readings
  114. 15: Time-Domain Spectroscopy
  115. 15.1: Absorption Spectra from Time-Correlation Functions
  116. 15.2: Describing Diverse Spectroscopies with the Dipole Correlation Function
  117. 15.3: Vibrational and Rotational Spectroscopy
  118. 15.4: Line Broadening Mechanisms
  119. 15.5: Readings
  120. 16: Coupling of Electronic and Nuclear Motion
  121. 16.1: The Displaced Harmonic Oscillator Model
  122. 16.2: Coupling to a Harmonic Bath
  123. 16.3: Semiclassical Approximation to the Dipole Correlation Function
  124. 16.4: Readings
  125. 17: Fluctuations and Dephasing
  126. 17.1: Line-broadening, dephasing, and spectral diffusion
  127. 17.2: Gaussian-Stochastic Model for Spectral Diffusion
  128. 17.3: The Energy Gap Hamiltonian
  129. 17.4: Spectral Density for Condensed Phase Spectroscopy
  130. 17.5: The Harmonic Bath’s Relation to the Langevin Equation
  131. 17.6: Readings
  132. 18: Quantum Relaxation Processes
  133. 18.1: Vibrational Relaxation
  134. 18.2: Golden Rule Vibrational Relaxation Rates
  135. 18.3: Multiquantum relaxation of polyatomic molecules
  136. 18.4: Redfield Theory and Master Equation
  137. 18.5: Readings
  138. 19: Energy and Charge Transfer
  139. 19.1: Intermolecular Electronic Interactions
  140. 19.2: Resonance Energy Transfer and Transition Dipole Coupling
  141. 19.3: Förster Resonance Energy Transfer
  142. 19.4: Marcus Theory for Electron Transfer
  143. 19.5: Readings
  144. 20: Excitons
  145. 20.1: What are excitons?
  146. 20.2: Frenkel excitons in molecular aggregates
  147. 20.3: Absorption spectrum of a dimer
  148. 20.4: Absorption spectra of J aggregates
  149. 20.5: Frenkel exciton transport
  150. 20.6: Tight-binding model
  151. 20.7: Readings
  152. 21: Appendices
  153. 21.1: Math and Physics Reference Material
  154. 21.1.1: Atomic Units
  155. 21.1.2: Dirac Delta Function
  156. 21.1.3: Gaussian Integrals and Error Function
  157. 21.2: Quantum Mechanics- Extra Topics
  158. 21.2.1: Numerically Solving the Schrödinger Equation
  159. 21.2.2: Separation of Subsystems
  160. 21.2.3: Morse Oscillator
  161. Back Matter
  162. Notation and variables used
  163. Index
  164. Glossary
  165. Detailed Licensing