Students are encouraged to print and read the course lecture notes in advance of lectures.
A listing of lecture session topics and corresponding lecture notes is included in the table below. In addition, an overall table of contents for the lecture notes is presented.
Lecture notes files
| Lec # |
Topics |
| 1 |
Time-Independent Hamiltonian; Two-Level System; Density Matrix (PDF) |
| 2 |
Time-Development of State Amplitudes: Resonant Driving of a Two-Level System (PDF) |
| 3 |
Quantum Dynamics; The Time-Evolution Operator (PDF) |
| 4 |
The Schrödinger, Heisenberg, and Interaction Pictures (PDF) |
| 5 |
Perturbation Theory I (PDF) |
| 6 |
Perturbation Theory II |
| 7 |
Fermi's Golden Rule (PDF) |
| 8 |
Irreversible Relaxation (PDF) |
| 9 |
Interaction of Light and Matter; Electric Dipole Hamiltonian (PDF) |
| 10 |
Electric Dipole Hamiltonian and Absorption of Light (PDF) |
| 11 |
Spectroscopy of Aggregates (PDF) |
| 12 |
Spectroscopy of Aggregates (cont.) |
| 13 |
Time-Correlation Functions (PDF 1) (PDF 2) |
| 14 |
Absorption Lineshape from Time-Correlation Functions (PDF) |
| 15 |
Electronic Spectroscopy: The Displaced Harmonic Oscillator Model (PDF) |
| 16 |
Displaced Harmonic Oscillator |
| 17 |
Displaced Harmonic Oscillator (cont.) |
| 18 |
Lineshapes: Fluctuation and Relaxation (PDF) |
| 19 |
Quantum Fluctuations (PDF) |
| 20 |
Vibrational Relaxation (PDF) |
| 21 |
Förster Theory and Marcus Theory (PDF) |
| 22 |
Linear Response Theory (PDF 1 of 2) (PDF 2 of 2) |
| 23 |
Nonlinear Spectroscopy I (PDF) |
| 24 |
Nonlinear Spectroscopy II (PDF) |
| 25 |
Nonlinear Spectroscopy III (PDF) |
| 26 |
Nonlinear Spectroscopy IV |
Lecture Notes Table of Contents
Course topics and readings
| Topics |
Lecture Notes Page # |
| Introduction |
| Time-Independent Hamiltonian |
1 |
| Two-Level System |
4 |
| Density Matrix |
9 |
| Appendix: Properties of Operators |
13 |
| Basics of Time-Dependent Hamiltonian |
| Resonant Driving of a Two-Level System |
14 |
| Quantum Dynamics: The Time-Evolution Operator |
20 |
| Schrödinger, Heisenberg and Interaction Pictures |
29 |
Perturbation Theory
First Order Perturbation Theory |
37
43 |
| Fermi's Golden Rule |
52 |
| Irreversible Relaxation |
60 |
| Light-Matter Interaction |
Interaction of Light and Matter
Electric Dipole Hamiltonian and Absorption Spectrum
Relaxation and Line Broadening of Spectrum |
66
72
74 |
| Supplement: Review of Free Electromagnetic Field |
76 |
Absorption and Stimulated Emission
Spontaneous Emission |
81
84 |
| Quantized Radiation Field |
86 |
| Absorption Spectra of Molecular Aggregates |
97 |
| Spectroscopy Using Time-Correlation Functions |
| Time-Correlation Functions |
110 |
| Supplement: Space Correlation Functions |
|
Absorption Lineshape from Time-Correlation Functions
Examples: Vibrational, Rotational, Raman Spectroscopy |
125
129 |
| Ensemble Averaging and Line Broadening |
131 |
Electronic Spectroscopy
The Displaced Harmonic Oscillator Model
Franck-Condon Transitions
Finite Temperature and Coupling to a Distribution |
133
139
142 |
| Förster Theory and Marcus Theory |
146 |
| Fluctuations and Relaxation Rates |
Fluctuations and Spectral Diffusion
Gaussian-Stochastic Model for Lineshape
Appendix: Cumulant Expansion |
152
154
160 |
Quantum Treatment of Fluctuations
Energy Gap Hamiltonian
Brownian Oscillator Model |
162
164
173 |
| Vibrational Relaxation |
175 |
| Linear Response Theory |
Classical Treatment
Linear Response Functions and Susceptibility
Kramers-Krönig Relations
Nonlinear Response Functions |
181
186
188 |
| Quantum Response Functions |
189 |
Response Function and Energy Absorption
Relaxation of Prepared State and Fluctuation-Dissipation |
193
196 |
| Coherent Nonlinear Spectroscopy |
Nonlinear Polarization
Propagating the Density Matrix |
198
207 |
| Diagrammatic Perturbation Theory |
209 |
Third-Order Nonlinear Spectroscopy Photon Echo
Transient Grating
CARS
Pump-Probe |
212
217
218
220
221 |
| Characterizing Fluctuations with Nonlinear Spectroscopy |
223 |
Acknowledgements
The notes for this course have been developed from many materials. In large part this includes the references for the course, as noted in the readings. I would like to thank a number of colleagues and prior instructors who provided notes that guided the preparation of many of these lectures, including Bob Silbey, Keith Nelson, Bob Field, John Ross and Graham Fleming. I also want to thank Anne Hudson for her invaluable assistance in preparing the notes.