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Time Dependent Quantum Mechanics and Spectroscopy
These notes are meant as a resource for chemists that study the time-dependent quantum mechanics, dynamics, and spectroscopy of molecular systems.
- Author
- Andrei Tokmakoff
- Publisher
- University of Chicago
- Source
- LibreTexts
- License
- CC BY-NC-SA
- Language
- EN
- Category
- Basic Sciences
Contents· 80 sections
- 01: Overview of Time-Independent Quantum Mechanics
- 1.01: Describing a System Quantum Mechanically
- 1.02: Matrix Mechanics
- 1.03: Basic Quantum Mechanical Models
- 1.04: Exponential Operators
- 1.05: Numerically Solving the Schrodinger Equation
- 02: Introduction to Time-Dependent Quantum Mechanics
- 2.01: Time-Evolution with a Time-Independent Hamiltonian
- 2.02: Exponential Operators
- 2.03: Two-Level Systems
- 03: Time-Evolution Operator
- 3.01: Time-Evolution Operator
- 3.02: Integrating the Schrodinger Equation Directly
- 3.03: Transitions Induced by Time-Dependent Potential
- 3.04: Resonant Driving of a Two-Level System
- 3.05: Schrodinger and Heisenberg Representations
- 3.06: Interaction Picture
- 3.07: Time-Dependent Perturbation Theory
- 3.08: Fermis Golden Rule
- 04: Irreversible Relaxation
- 4.01: Introduction to Dissipative Dynamics
- 05: The Density Matrix
- 5.01: Introduction to the Density Matrix
- 5.02: Time-Evolution of the Density Matrix
- 5.03: The Density Matrix in the Interaction Picture
- 06: Adiabatic Approximation
- 6.01: BornOppenheimer Approximation
- 6.02: Nonadiabatic Effects
- 6.03: Diabatic and Adiabatic States
- 6.04: Adiabatic and Nonadiabatic Dynamics
- 6.05: LandauZener Transition Probability
- 07: Interaction of Light and Matter
- 7.01: Introduction to Light-Matter Interactions
- 7.02: Classical LightMatter Interactions
- 7.03: Quantum Mechanical Electric Dipole Hamiltonian
- 7.04: Relaxation and Line-Broadening
- 7.05: Absorption Cross-Sections
- 7.06: Appendix - Review of Free Electromagnetic Field
- 7.07: Appendix - Magnetic Dipole and Electric Quadrupole Transitions
- 08: Mixed States and the Density Matrix
- 8.01: Mixed States
- 8.02: Density Matrix for a Mixed State
- 09: Irreversible and Random Processes
- 9.01: Concepts and Definitions
- 9.02: Thermal Equilibrium
- 9.03: Fluctuations
- 10: Time-Correlation Functions
- 10.01: Definitions Properties and Examples of Correlation Functions
- 10.02: Correlation Function from a Discrete Trajectory
- 10.03: Quantum Time-Correlation Functions
- 10.04: Transition Rates from Correlation Functions
- 11: Linear Response Theory
- 11.01: Classical Linear Response Theory
- 11.02: Quantum Linear Response Functions
- 11.03: The Response Function and Energy Absorption
- 11.04: Relaxation of a Prepared State
- 12: Time-domain Description of Spectroscopy
- 12.01: A Classical Description of Spectroscopy
- 12.02: Time-Correlation Function Description of Absorption Lineshape
- 12.03: Different Types of Spectroscopy Emerge from the Dipole Operator
- 12.04: Ensemble Averaging and Line-Broadening
- 13: Coupling of Electronic and Nuclear Motion
- 13.01: The Displaced Harmonic Oscillator Model
- 13.02: Coupling to a Harmonic Bath
- 13.03: Semiclassical Approximation to the Dipole Correlation Function
- 14: Fluctuations in Spectroscopy
- 14.01: Fluctuations and Randomness - Some Definitions
- 14.02: Line-Broadening and Spectral Diffusion
- 14.03: Gaussian-Stochastic Model for Spectral Diffusion
- 14.04: The Energy Gap Hamiltonian
- 14.05: Correspondence of Harmonic Bath and Stochastic Equations of Motion
- 15: Energy and Charge Transfer
- 15.01: Electronic Interactions
- 15.02: Forster Resonance Energy Transfer (FRET)
- 15.03: Excitons in Molecular Aggregates
- 15.04: Multiple Particles and Second Quantization
- 15.05: Marcus Theory for Electron Transfer
- 16: Quantum Relaxation Processes
- 16.01: Vibrational Relaxation
- 16.02: A Density Matrix Description of Quantum Relaxation