Quantum Dynamics and Spectroscopy
A Summer Short Course on Quantum Dynamics and Spectroscopy ( Lectured in Chinese)
8 unitsThis is to be a short course of 8 lectures that provide a general overview of timedependent quantum mechanics and approximation methods useful in descriptions of excitation energy transfer and electron transfer in condensedphase molecular systems. A densitymatrix approach will be emphasized, and the content will consist of developments of theoretical methods that have broad applications in physical chemistry. A timedependent approach to linear spectroscopy and a brief introduction to nonlinear spectroscopy will also be presented.
This is to be a short course of 8 lectures that provide a general overview of timedependent quantum mechanics and approximation methods useful in descriptions of excitation energy transfer and electron transfer problems in condensedphase molecular systems. A densitymatrix approach will be emphasized, and the content will consist of developments of theoretical methods that have broad applications in physical chemistry. A timedependent approach to linear as well as nonlinear spectroscopy will be presented.
The course is designed to help students establish the basic capacity to carry out theoretical research in the field of quantum dynamics and spectroscopy.
Attendants should have been familiar with notions of timeindependent quantum mechanics such as
* Timeindependent Schrodinger equation & simple quantum systems
* Dirac notation & basics of matrix mechanics
* Operators, second quantization notations
Each meeting will be about 2 hours, and the lectures will focus on covering the principle theoretical ideas in each topic listed in the following:
 Timedependent perturbation theory
 Fermi's golden rule and density matrix formalism
 Systembath model and quantum master equations
 Timecorrelation functions (8/19, 2:00PM, Rm. 121)
 Redfield theory for excitation energy transfer & electron transfer
 Timedomain description of linear spectroscopy
 Introduction to nonlinear spectroscopy
 Twodimensional electronic spectroscopy
Schatz & Ratner's "Quantum Mechanics in Chemistry" by George C. Schatz (Author), Mark A. Ratner (Author)
Publisher: Dover Publications
ISBN: 9780486420035
Week  Topics  Reference 

0  Prerequisites: Attendants should have been familiar with notions of timeindependent quantum mechanics such as * Timeindependent Schrodinger equation & simple quantum systems * Dirac notation & basics of matrix mechanics * Operators, second quantization notations 

1  Timedependent perturbation theory * Timedependent Schrodinger equation * "Pictures" of quantum dynamics * Interaction picture & timedependent perturbation theory 

2  Fermi's golden rule and density matrix formalism * Fermi's Golden Rule * Ensemble & averaging in chemical physics * Density matrix formalism * Twolevel system: eigenvalues, eigenvectors, time evolution, and thermal equilibrium. 

3  Systembath model and quantum master equations * Systembath model & Thermal average * Cumulant expansion & Gaussian fluctuation approximation * Formal derivation of a timelocal quantum master equation 

4  Timecorrelation Functions * Quantum timecorrelation functions * Properties of timecorrelation functions * Example: positionposition TCF for harmonic oscillators. 

5  Redfield theory for excitation energy transfer & electron transfer * Frenkel exciton Hamiltonian * Driving force for excitation energy transfer & electron transfer * Timelocal Markovian quantum master equation for EET (Redfield theory) * Population dynamics & detailed balance 

6  Timedomain description of linear spectroscopy * Lightmatter interactions * Lineshape function & linear absorption/emission spectrum * Displaced harmonic oscillator model * The energygap Hamiltonian 

7  Introduction to nonlinear spectroscopy  
8  Twodimensional electronic spectroscopy 
Lecture  Handout 

Lecture 1  Timedependent perturbation theory 
Lecture 2  Fermi's golden rule and density matrix formalism 
Lecture 3  Condensedphase Quantum Dynamics 
Lecture 4  Timecorrelation functions 
Lecture 5  Redfield theory for excitation energy transfer & electron transfer 
Lecture 6  Timedomain Description of Linear Spectroscopy 
Lecture 7  Nonlinear Spectroscopy 
Lecture 8  Photonecho & Twodimensional Electronic Spectroscopy 
Lecture  Topic  length 

Lecture 1  Timedependent perturbation theory  1:43:26 
Lecture 2  Fermi's golden rule and density matrix formalism  1:49:51 
Lecture 3  Systembath model and quantum master equations  1:44:52 
Lecture 4  Timecorrelation functions  1:46:57 
Lecture 5  Redfield theory for excitation energy transfer & electron transfer  2:17:42 
Lecture 6  Timedomain description of linear spectroscopy  2:04:09 
Lecture 7  Introduction to nonlinear spectroscopy  1:24:04 
Lecture 8  Twodimensional electronic spectroscopy  1:41:32 
Lecture  Topics  Reference 

Lecture 0  Prerequisites 

Lecture 3  Condensedphase Quantum Dynamics 

Lecture 4  Timecorrelation functions 

Lecture 5  Redfield theory for excitation energy transfer & electron transfer 

Lecture 6  Timedomain Description of Linear Spectroscopy 

Lecture 7  Nonlinear Spectroscopy 

Lecture 8  Photonecho & Twodimensional Electronic Spectroscopy 

2019© YuanChung Cheng's Research Group  鄭原忠老師理論物理化學研究室
國立臺灣大學化學系  Department of Chemistry, National Taiwan University