|
Week of August 30 - Lectures 1, 2 Newtonian mechanics; generalized coordinates; Variational principles; Lagrangian, Hamiltonian equations of motion; Poisson brackets ------------------
Week of September 6 - Lectures 3, 4 Postulates of quantum mechanics: linear vector spaces; eigenfunctions and eigenvalues; abstract state vectors; coordinate representation and the Schrödinger equation; operators, scalar products; Dirac notation ------------------
Week of September 13 - Lectures 5, 6, 7 Wavefunctions; commutation relations; expectation values; stationary states; Hermitian operators; complete sets of commuting observables; Uncertainty principle; Ehrenfest theorem ------------------
Week of September 20 - Lectures 8, 9, 10 Matrices in quantum mechanics; completeness relation for discrete states; secular determinants and matrix diagonalization: similarity transformations. Dirac delta-function; completeness relation for continuous states; time-evolution and propagators; Feynman path integral approach and the classical limit ------------------
Week of September 27 - Lectures 11, 12 Free translation in one dimension; flux density - equation of continuity; wave packets; particle at a potential barrier ------------------
Week of October 4 - Lectures 13, 14 Transmission coefficients and resonances; particle in an infinite square well; 1-dimensional harmonic oscillator: factorization of the Schrödinger equation. Creation and annihilation operators ------------------
Week of October 11 - Lectures 15, 16, 17 Hermite differential equation; classically forbidden motion; Correspondence principle; properties of harmonic oscillator wavefunctions. Angular momentum: operators and commutation relations ------------------
Week of October 18 - Lectures 18, 19, 20 Curvilinear coordinates; eigenfunctions of L2, Lz; space quantization. Raising, lowering operators for angular momentum. Legendre polynomials, spherical harmonics. Two- particle dynamics: rigid rotor ------------------
Week of October 25 - Lectures 21, 22 The hydrogen atom: Laguerre differential equation. Boundary conditions and the Rydberg energy spectrum. Radial and angular wavefunctions ------------------
Week of November 1 - Lectures 23, 24, 25 Radial and angular wavefunctions. Clebsch-Gordan series. Time-independent perturbation theory: Rayleigh-Schrödinger formalism; 1st, 2nd order corrections to energy, wavefunction ------------------
Week of November 8 - Lectures 26, 27, 28 Degenerate perturbation theory: Stark effect in the hydrogen atom.The Variation Theorem. Variation with respect to a parameter. Variation with respect to a basis set - secular equation ------------------
Week of November 15 - Lectures 29, 30, 31 Hellman-Feynman Theorem. Time-dependent perturbation theory: coupled equations, Dirac variation of constants method; two-level systems: "switched-on" constant perturbation. Laplace transform solution to coupled equations. Rabi oscillations. Harmonic perturbation - semiclassical radiation theory. Fermi's Golden Rule. Einstein A- and B- coefficients ------------------
Week of November 22 - Lectures 32, 33 Many-electron systems: electron spin and the Pauli Exclusion Principle; Slater determinants; excited states of helium: singlets and triplets ------------------
Week of November 29 - Lectures 34, 35, 36 The Self-Consistent Field approximation; matrix elements of Slater determinants: Hartree and Hartree-Fock independent particle methods. Density functional theory: Hohenberg-Kohn theorem, Kohn-Sham equations ------------------
Week of December 6 - Lectures 37, 38, 39 ------------------
|