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G25.2666: Quantum Chemistry and Dynamics
Spring 2005, TTh 4:55-6:10
Professor M. Tuckerman
Office: 1001L Main
Phone: 998-8471
E-mail: mark.tuckerman@nyu.edu
Textbook:
Introduction to Quantum Mechanics in Chemistry M. A. Ratner
and G. C. Schatz, Prentice Hall (2000).
Quantum Mechanics in Chemistry M. A. Ratner
and G. C. Schatz, Prentice Hall (1993).
Some additional material will be drawn from other sources including:
Principles of Quantum Mechanics R. Shankar, Plenum Press (1984)
Course Outline
-
- I.
- The simplest chemical bond: The H
ion.
- A.
- Procedure for exact treatment
- B.
- Review of variational theory
- C.
- Variational treatment
- D.
- Bonding and anti-bonding orbitals
- II.
- General theory of spin:
- A.
- Experimental evidence for electron spin.
- B.
- Spin operators and the spin Hilbert space.
- C.
- Rotation of spin states:
- 1.
- Some group theoretic concepts.
- D.
- Natural occurrence of spin in the Dirac theory.
- III.
- Systems of identical particles:
- A.
- Classical vs. quantum descriptions.
- B.
- Permutation operators and manybody wavefunctions.
- C.
- Bosons and fermions.
- E.
- Second quantization.
- IV.
- Molecular quantum mechanics:
- A.
- The Born-Oppenheimer approximation
- B.
- The Hellman-Feynman theorem
- C.
- Wavefunction based methods
- 1.
- Hartree-Fock theory
- 2.
- Perturbation theory
- 3.
- Configuration Interaction
- 4.
- Multi-configuration SCF
- 5.
- Coupled Cluster Methods
- D.
- Density functional theory
- E.
- Semi-empirical methods
- F.
- Introduction to group theory and its applications in molecular quantum mechanics
- V.
- Time-dependent perturbation theory:
- A.
- Shcrödinger, Heisenberg and interaction pictures.
- B.
- Approximate solution of the time-dependent Schrödinger equation.
- 1.
- Time-ordered exponentials.
- 2.
- Transition probabilities.
- 3.
- Fermi's Golden Rule.
- VI.
- Interaction of matter with an electromagnetic field: Spectroscopy
- A.
- Introduction to classical electrodynamics
- B.
- The photoelectric effect in hydrogen
- C.
- Absorption/emission spectroscopy in molecules
- D.
- Light Scattering
- E.
- Vibrational spectroscopy
- VII.
- Scattering theory:
- A.
- Scattering cross sections.
- B.
- Stationary scattering states.
- C.
- The scattering amplitude.
- D.
- Green's function approach to scattering:
- 1.
- The Born approximation
- E.
- Scattering from a central potential:
- 1.
- The partial wave expansion.
- 2.
- Spherical waves.
- 3.
- Phase shifts.
- VIII.
- The Feynman path integral formulation of quantum mechanics:
- A.
- Coordinate space representation of the propagator.
- B.
- Formulation of the propagator as a sum over paths.
- 1.
- Discrete and continuous representations.
- 2.
- Functional integrals.
- 3.
- Real and imaginary time path integrals.
- C.
- Applications of the path-integral in reaction-rate theory
Grading basis
-
- Homework:............20%
-
- Midterm:...............40%
-
- Final:....................40%
Notes for all (hopefully) lectures can be found on the course web page:
http://www.nyu.edu/classes/tuckerman/quant.mech
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Mark Tuckerman
2005-01-27