Review of classical mechanics

      Newton's second law
      Generalized coordinates
      Lagrange's equations (from N's laws)
      Conjugate momentum
            Canonically conjugate variables
      Hamiltonian (as Legendre transformation)
      Poisson brackets
            { , } of canonically conjugate variables
      Equations of motion in Poisson bracket form
      Time dependence of an observable in Poisson bracket form


Quantization

      Poisson brackets & commutators
      Commutators of canonical pairs
      Operators
      Representations of operators
            Construction of operators for observables
            Hamiltonian operator
      State spaces
            Function spaces
            Vector spaces
      Dirac notation
            closure, etc
      Hermitian operators
      Unitary operators
      x and p representations, delta functions
            Relation between kets and wave functions
            Fourier transforms in x and p
      Heisenberg equations of motions
      Time development operators (propagators)
            Schroedinger equation for U
            Schroedinger equation for functions and vectors
      Stationary states
            Eigenstates, eigenvalues
            Completeness
      Expectation values
      Pictures ("Representations")
            Schroedinger
            Heisenberg
            Interaction
            Others

      Solution of the time-dependent Schroedinger equation
            Power series expansion
            Time-dependent perturbation theory
            Magnus (and etc.) expansions
            polarizability


Harmonic Oscillator

      Operator (matrix) approach
      Creation and annihilation operators
      Eigenvalue spectrum
      Matrices and matrix elements
      Harmonically driven harmonic oscillator
      Relationship to classical harmonic oscillator


Angular momentum

      Operator (matrix) approach
      Raising and lowering operators
      Eigenvalue spectra
      Matrices and matrix elements
            Pauli matrices
            Symmetric top
      Configuration space eigenfunctions (from matrices)


How to quantize a new system

      Lagrangian formulation
      Examples
            Particle on a helix (optical activity)
            Particle in a (classical) E-M field
                  Coulomb and Lorentz gauges
                  Goeppert-Mayer transformation
            Quantization of the E-M field
                  field modes
                  photons


Radiative decay

      Jaynes theory (wrong, but cute and instructive)
      Einstein "A" coefficient


Rotating wave approximation

      Dynamics of a two-level system
      Rabi theory

Formal Hartree-Fock theory

      Fock space
      Fermi creation and annihilation operators
            One- and two-electron operators
      Hamiltonian in Fock space representation
      core electrons
      Fock matrix
      definition of the Hartree-Fock orbitals
            Brillouin's theorem
      Koopman's theorem


Applied ab initio theory

      Practical Hartree-Fock
      Configuration interaction
      Coupled-Cluster theory
      Density Functional theory

Administrative Details

      Exams
            Midterm, 11 Mar (tentative)
            Final, 11 May, (alternate, 7 May)

      Homework
            12 - 14 problem sets

      Grading
            20% midterm
            30% final
            50% problem sets

References

The following books are on reserve in the Main Library

Our text book is:
C. Cohen-Tannoudji, et al. Quantum Mechanics, vols 1 and 2, QC 174.12 C6313

Other useful references:
H. Goldstein, Classical Mechanics, QA 805 G6

A, Messiah, Quantum Mechanics vols 1 and 2, QC 174.1 M413 v1 & v2

P. A. M. Dirac, Principles of Quantum Mechanics, QC 174.3 D5 1958

H. Eyring, et al, Quantum Chemistry, QD 453 E9

L. Schiff, Quantum Mechanics, QC 174.1 S34

S. Schweber, An Introduction to Relativistic Quantum Field Theory, 530.12 S412