5.74 | Spring 2004 | Graduate

Introductory Quantum Mechanics II

Readings

Recommended texts, general references, and other references are listed below the table.

Lec # TOPICS READINGS
1

Time-Independent Hamiltonian

Two-Level System

Density Matrix

Two Level System

Mukamel, S. Chapter 2 in Principles of Nonlinear Optical Spectroscopy. New York, NY: Oxford University Press, 1995.

Cohen-Tannoudji, Claude, Bernard Diu, and Franck Laloë. Quantum Mechanics. 2nd ed. Vols. 1 and 2. Paris, France: Wiley-Interscience, 2006, pp. 405, and 420. ISBN: 9780471569527.

Density Matrix

Blum, K. Density Matrix Theory and Applications. New York, NY: Plenum Press, 1981.

Ernst, R. R., G. Bodenhausen, and A. Wokaun. Principles of Nuclear Magnetic Resonance in One and Two Dimensions. New York, NY: Oxford University Press, 1987.

McHale, J. L. Molecular Spectroscopy. Upper Saddle River, NJ: Prentice Hall, 1999.

Sakurai, J. J. Modern Quantum Mechanics. Reading, MA: Addison-Wesley, 1994.

2 Quantum Dynamics; Time-Evolution Operator

Merzbacher, E. Chapter 14 in Quantum Mechanics. 3rd ed. New York, NY: Wiley, 1998.

Sakurai, J. J. Chapter 2 in Modern Quantum Mechanics. Reading, MA: Addison-Wesley, 1994.

Mukamel, S. Principles of Nonlinear Optical Spectroscopy. New York, NY: Oxford University Press, 1995.

Cohen-Tannoudji, Claude, Bernard Diu, and Franck Laloë. Quantum Mechanics. 2nd ed. Vols. 1 and 2. Paris, France: Wiley-Interscience, 2006, p. 308. ISBN: 9780471569527.

3 Schrödinger/Heisenberg/Interaction Pictures

Sakurai, J. J. Chapter 2 in Modern Quantum Mechanics. Reading, MA: Addison-Wesley, 1994.

Mukamel, S. Principles of Nonlinear Optical Spectroscopy. New York, NY: Oxford University Press, 1995.

Cohen-Tannoudji, Claude, Bernard Diu, and Franck Laloë. Quantum Mechanics. 2nd ed. Vols. 1 and 2. Paris, France: Wiley-Interscience, 2006, p. 312. ISBN: 9780471569527.

4 Time-development of State Amplitudes/Resonant Driving of Two-Level System

Sakurai, J. J. Modern Quantum Mechanics. Reading, MA: Addison-Wesley, 1994.

Cohen-Tannoudji, Claude, Bernard Diu, and Franck Laloë. Quantum Mechanics. 2nd ed. Vols. 1 and 2. Paris, France: Wiley-Interscience, 2006, p. 1340. ISBN: 9780471569527.

5 Perturbation Theory

Sakurai, J. J. Modern Quantum Mechanics. Reading, MA: Addison-Wesley, 1994.

Cohen-Tannoudji, Claude, Bernard Diu, and Franck Laloë. Quantum Mechanics. 2nd ed. Vols. 1 and 2. Paris, France: Wiley-Interscience, 2006, p. 1285. ISBN: 9780471569527.

6 Fermi’s Golden Rule

Supplement: Slowly Applied Perturbation

Fermi’s Golden Rule

McHale, J. L. Chapter 4 in Molecular Spectroscopy. Upper Saddle River, NJ: Prentice Hall, 1999.

Sakurai, J. J. Modern Quantum Mechanics. Reading, MA: Addison-Wesley, 1994.

Cohen-Tannoudji, Claude, Bernard Diu, and Franck Laloë. Quantum Mechanics. 2nd ed. Vols. 1 and 2. Paris, France: Wiley-Interscience, 2006, p. 1299. ISBN: 9780471569527.

Slowly Applied Perturbation

Sakurai, J. J. Modern Quantum Mechanics. Reading, MA: Addison-Wesley, 1994.

7 Irreversible Relaxation

Merzbacher, E. Quantum Mechanics. 3rd ed. New York, NY: Wiley, 1998, p.510.

Cohen-Tannoudji, Claude, Bernard Diu, and Franck Laloë. Quantum Mechanics. 2nd ed. Vols. 1 and 2. Paris, France: Wiley-Interscience, 2006, p. 1344. ISBN: 9780471569527.

8

Interaction of Light and Matter

Supplement: Review of Electromagnetic Fields

Interaction of Light and Matter

Baym, G. Lectures on Quantum Mechanics. London, UK: Benjamin/Cummings, 1969.

Cohen-Tannoudji, Claude, Bernard Diu, and Franck Laloë. Quantum Mechanics. 2nd ed. Vols. 1 and 2. Paris, France: Wiley-Interscience, 2006. ISBN: 9780471569527.

McHale, J. L. Molecular Spectroscopy. Upper Saddle River, NJ: Prentice Hall, 1999.

Merzbacher, E. Quantum Mechanics. 3rd ed. New York, NY: Wiley, 1998.

Sakurai, J. J. Modern Quantum Mechanics. Reading, MA: Addison-Wesley, 1994.

Supplement: Review of Electromagnetic Fields

Jackson, J. D. Chapter 6 and 7 in Classical Electrodynamics. New York, NY: Wiley.
Chapter 6 describes vector and scalar potentials, and Chapter 7 talks about plane waves.

9 Time-Correlation Functions  
10 Absorption Lineshape from Time-Correlation Functions  
11 Electronic Spectroscopy: The Displaced Harmonic Oscillator Model  
12 Lineshapes: Fluctuation and Relaxation  
13 Förster Theory and Marcus Theory  
14 Angular Momentum in Spherical Tensor Operations Blum, K. Section 9.3.2.1 in Density Matrix Theory and Applications. New York, NY: Plenum Press, 1981.
15 3-j and 6-j Coefficients Oxtoby, D. W. “Vibrational Population Relaxation in Liquids.” Sections 3.5, 4.1, and 5.1 in Adv Chem Phys 47 (1981): 487-519.
16 Hund’s Coupling Cases: Transformations of Basis Set Oxtoby, D. W. “Vibrational Population Relaxation in Liquids.” Sections 3.5, 4.1, and 5.1 in Adv Chem Phys 47 (1981): 487-519.
17 Bright State, Dark State, Pluck Blum, K. Sections 9.1.1 and 9.4.4 in Density Matrix Theory and Applications. New York, NY: Plenum Press, 1981.
18 Frequency Domain Spectrum as FT of Autocorrelation Function Blum, K. Section 9.1.3 in Density Matrix Theory and Applications. New York, NY: Plenum Press, 1981.
19 Dynamical Quantities: Visualization of Dynamics
 
Blum, K. Section 9.1.4 in Density Matrix Theory and Applications. New York, NY: Plenum Press, 1981.
20 Motion of Center of Wavepacket Blum, K. Section 9.1.7 in Density Matrix Theory and Applications. New York, NY: Plenum Press, 1981.
21 Resonance Operators: Equation of Motion Blum, K. Sections 9.1.8 and 9.4.9 in Density Matrix Theory and Applications. New York, NY: Plenum Press, 1981.
22 From Quantum Beats to Wavepackets Blum, K. Sections 9.2.1-2 in  Density Matrix Theory and Applications. New York, NY: Plenum Press, 1981.
23

Types of Wavepacket

Supplement: Stationary Phase for Vibration-Electronic Spectra and Heller’s Fractionation Index

Blum, K. Sections 9.3-4 in Density Matrix Theory and Applications. New York, NY: Plenum Press, 1981.
24 Complex Energy Heff: Nondegenerate Perturbation Theory
 
Blum, K. Section 9.3 in Density Matrix Theory and Applications. New York, NY: Plenum Press, 1981.
25

Quasi-degenerate Perturbation Theory

Strong and Weak Coupling Limits

Blum, K. Section 9.3 in Density Matrix Theory and Applications. New York, NY: Plenum Press, 1981.
26 Polyads, a, a+, N
 
Blum, K. Sections 9.4.4 - 9.4.9 in Density Matrix Theory and Applications. New York, NY: Plenum Press, 1981.
27 Dynamics in State Space and in Q, P Space Blum, K. Sections 9.4.7, 9.4.8, and 9.4.11 in Density Matrix Theory and Applications. New York, NY: Plenum Press, 1981.
28

Chem. Phys. Lett. 320 (2000): 553

Visualizing IVR

Blum, K. Sections 9.4.9, and 9.4.10 in Density Matrix Theory and Applications. New York, NY: Plenum Press, 1981.
29 Normal-Local Modes: Classical, Morse, Minimal Model Blum, K. Sections 9.4.12.1-4 in Density Matrix Theory and Applications. New York, NY: Plenum Press, 1981.
30 Normal-Local Modes: 6-Parameter Models Blum, K. Section 9.4.12.5 in Density Matrix Theory and Applications. New York, NY: Plenum Press, 1981.
31 From Quantum Mechanical Heff to Classical Mechanical Heff
 
Blum, K. Section 9.4.13 in Density Matrix Theory and Applications. New York, NY: Plenum Press, 1981.
32

IVR, ISC, IC

Extra Topics

Diabatic-Adiabatic

Electromagnetic Field-Dressed Potential Curves

Coherent Control of Photofragment Branching Ratios

IVR, ISC, IC

Blum, K. Sections 9.4.14-15 in Density Matrix Theory and Applications. New York, NY: Plenum Press, 1981.

Diabatic-Adiabatic

Blum, K. Sections 3.31-3.34 in Density Matrix Theory and Applications. New York, NY: Plenum Press, 1981.

Electromagnetic Field-Dressed Potential Curves

Blum, K. Section 3.35 in Density Matrix Theory and Applications. New York, NY: Plenum Press, 1981.

Coherent Control of Photofragment Branching Ratios

Blum, K. Section 8.13 in Density Matrix Theory and Applications. New York, NY: Plenum Press, 1981.

  Final Exam  

Texts

McHale, J. L. Molecular Spectroscopy. Upper Saddle River, NJ: Prentice Hall, 1998.  ISBN: 9780132290630.
This text covers light matter interactions, correlation functions, and various molecular spectroscopies.

Mukamel, S. Principles of Nonlinear Optical Spectroscopy. New York, NY: Oxford University Press, 1999. ISBN: 9780195132915.
This is an advanced text that treats quantum dynamics, correlation functions, response functions, coupling of a system to a bath, and nonlinear spectroscopy.

General References

Baym, G. Lectures on Quantum Mechanics. Boulder, CO: Westview Press, 1974. ISBN: 9780805306675.

Ernst, R. R., G. Bodenhausen, and A. Wokaun. Principles of Nuclear Magnetic Resonance in One and Two Dimensions. New York, NY: Oxford, 1987. ISBN: 9780198556299.
Includes discussion of time-evolution in quantum systems, correlation functions, linear response.

McQuarrie, D. A. Statistical Mechanics. Sausalito, CA: University Science Books, 2000. ISBN: 9781891389153.
Useful for correlation function description of spectroscopy.

Merzbacher, E. Quantum Mechanics. 3rd ed. New York, NY: Wiley, 1997. ISBN: 9780471887027.
General physics text for quantum dynamics, perturbation theory, light matter interactions.

Sakurai, J. J. Modern Quantum Mechanics. Reading, MA: Addison-Wesley, 1994. ISBN: 9780201539295.

Other References

Electromagnetic Waves:

Jackson, J. D. Classical Electrodynamics. New York, NY: Wiley, 1998.  ISBN: 9780471309321.
Useful for light-matter interactions. Chapter 6 describes vector and scalar potentials and chapter 7 talks about plane waves.

Correlation Functions and Linear Response Theory:

Eyring, Henry, D. Henderson, and W. Jost. Physical Chemistry: An Advanced Treatise. New York, NY: Academic Press, 1971. ISBN: 9780122456015.

Berne, B. J., and R. Pecora. Dynamic Light Scattering. Malabar, FL: R. E. Krieger Publishing Co., 1990. ISBN: 9780894644238.

Gordon, R. G. “Correlation Functions for Molecular Motion.” Adv Magn Reson 3, no.1 (1968).

Wang, C. H. Spectroscopy of Condensed Media: Dynamics of Molecular Interactions. Orlando, FL: Academic Press, 1985. ISBN: 9780127347806.

Zwanzig, R. “Time-Correlation Functions and Transport Coefficients in Statistical Mechanics.” Annu Rev Phys Chem 16 (1965): 67-102.

Density Matrix and Relaxation:

Slichter, Charles P. Principles of Magnetic Resonance with Examples from Solid State Physics. New York, NY: Harper & Row, 1963.
Useful for discussion of density matrix and relaxation.

Blum, K. Density Matrix Theory and Applications. New York, NY: Plenum Press, 1981.
Includes description of density matrix and relaxation.

Förster and Marcus Theory:

Barbara, P. F., T. J. Meyer, and M. A. Ratner. “Contemporary issues in electron transfer research.” J Phys Chem 100 (1996): 13148-13168.

Jortner, J. “Temperature Dependent Activation Energy for Electron Transfer between Biological Molecules.” J Chem Phys 64 (1976): 4860.

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