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540-outline - 4 Angular momentum Angular momentum operators...

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C HEMISTRY 540: Q UANTUM M ECHANICS Fall Semester 2011 Instructor: Professor Nancy Makri Lectures: Tues. & Thur. 9:30-10:50 a.m. in 164 Noyes Lab Course Outline 1. Introduction The two-slit experiment. The particle-wave nature of matter. The Schrödinger equation. 2. General structure and formalism of quantum mechanics Postulates of quantum mechanics. Dirac notation. Operators and commutator algebra. Position and momentum operators. Orthonormality, completeness and basis sets. Dirac’s delta function. Symmetries and conservation laws. Discrete vs. continuous spectra. Matrix formulation of quantum mechanics. Solution of the eigenvalue problem. Stationary states. 3. Exactly solvable time-independent problems Free particle and the momentum representation. Potential barriers. Particle in a box. Particle on a ring. The harmonic oscillator; raising and lowering operators. Probability density and quantum-classical correspondence. Separable multidimensional problems; degeneracy. Introduction to normal mode transformations. Tunneling; two-level systems and inversion splitting.
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Unformatted text preview: 4. Angular momentum Angular momentum operators; eigenvalues and eigenfunctions (spherical harmonics). Orbital angular momentum. The hydrogen atom. Spin. Exchange symmetry for identical particles; bosons and fermions. Slater determinants. 5. Time-independent approximation methods Perturbation theory (non-degenerate and degenerate). Projection operators and Green’s functions. The variational principle. Linear variations and basis set expansions. Self-consistent field theory. The Born-Oppenheimer approximation. Potential functions. 6. Introduction to time-dependent quantum mechanics The time-dependent Schrödinger equation. Stationary states. Evolution of non-stationary states. Time-evolution operator for time-independent Hamiltonians. The Schrödinger, Heisenberg and interaction representations. The Heisenberg equation of motion. Time evolution operator for time-dependent Hamiltonians. Time ordering and Dyson series....
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