Chem 794 Quantum Mechanics II Spring 2005 Chemistry 794 Quantum Mechanics II Spring 2005 Course outline 1. Density matrix • Pure vs mixed states. Ensemble interpretation. • Reduced density matrices. Entanglement. • Equations of motion. Analogy with classical mechanics. • Relaxation and decoherence. 2. Time-dependent phenomena • Evolution operator. Propagator and Green’s functions. • Three pictures: Schr¨odinger, Heisenberg, interaction. • 2-level system. Rotating wave approximation. Bloch equations. • Time-dependent perturbation theory. Harmonic perturbations. Resonant phenom- ena. Transitions to continuum; Golden rule. • Sudden approximation. • Adiabatic approximation. • Perturbation theory for density operator. Linear response. 3. Path integral formulation of quantum mechanics 4. Molecule-field interactions • Maxwell’s equations, scalar and vector potentials, gauge transformations, free field, and all that. • Hamiltonian for charged particle in field. • Perturbation in dipole approximation. • A and B coefficients. Selection rules. Sum rules. • Electric quadrupole and magnetic dipole transitions. • High-order perturbation theory and multiphoton processes. • Nonlinear spectroscopy. • Electric properties of molecules. Polarizability. • Magnetic properties of molecules. Magnetic susceptibility. Diamagnetism & para- magnetism. 5. Scattering Theory • Particle flux and scattering cross sections. G.S. Ezra 1 Cornell University Chem 794 Quantum Mechanics II Spring 2005 • Green’s functions and scattering problem. • Born approximation. • Partial wave analysis of wavefunction for central scattering potential. • Phase shifts and differential cross section. 6. Group theory in quantum mechanics • Groups; classes; cosets; representations; irreps; Schur’s lemma. • Great Orthogonality theorem. • Characters; character tables. • Representation theory and QM. Symmetry and degeneracy. • Projection operators. • Matrix elements of operators: selection rules. • Rotation group: spherical tensors; Wigner-Eckart theorem. If we have time: 7. Molecular vibrations • Born-Oppenheimer approximation. • Rotation-vibration separability. • Normal modes. • Vibration-rotation transitions. Selection rules. Polarization. G.S. Ezra 2 Cornell University.