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Day Date Topics Mon 27 Aug Introduction; The Stern-Gerlach Experiment and its implications for the structure of nature Wed 29 Aug Quiz 1; Analysis of the Stern-Gerlach Experiment, and the analogy with polarized light Thu 30 Aug The Formalism: Kets, bras, and operators Mon 3 Sep No Classes: Labor Day Wed 5 Sep Quiz 2; Class cancelled: Instructor on travel Thu 6 Sep Base kets and the matrix representation Thu 6 Sep 6pm Makeup Class (JRSC 1C13): Measurements and observables Mon 10 Sep Compatible and incompatible observables; the generalized uncertainty relation Mon 10 Sep 6pm Makeup Class (JRSC 1C13): Change of basis; Unitary operators Wed 12 Sep Quiz 3; Class cancelled: Instructor on travel Thu 13 Sep Class cancelled: Instructor on travel Mon 17 Sep The position representation and the translation operator Wed 19 Sep Quiz 4; Momentum as generator of translations; Canonical commutation relations Thu 20 Sep Wave functions of position and momentum, including three dimensions Mon 24 Sep Motion of a wave packet Wed 26 Sep Time evolution: The Hamiltonian as a generator of time translation; time dependence of expectation values; the “Energy/Time” uncertainty relation Thu 27 Sep Quiz 5; No lecture today: Instructor on travel Mon 1 Oct The Schrödinger and Heisenberg pictures Wed 3 Oct Quiz 6; Formulating the simple harmonic oscillator Thu 4 Oct Solving the simple harmonic oscillator with the operator formalism Tue 9 Oct Schrödinger’s wave equation and interpreting the wave function Wed 10 Oct Quiz 7; Classical connections: Ehrenfest’s Theorem; the Hamilton-Jacobi Equation Thu 11 Oct Solving the simple harmonic oscillator with Schrödinger’s Equation and generating functions Modern Quantum Mechanics, Sakurai & Napolitano, Chapters 1,2,3 December 2, 2012 PHYS 6510/4510 Quantum Mechanics I (Fall 2012) 2.2; 2.4 2.5 2.2; 2.3 2.3 2.4 2.2 1.6 1.7 1.7 2.1 1.6 1.3 1.4 1.4 1.5 1.1 1.2 Textbook 1.1 18 Oct 22 Oct 24 Oct 25 29 29 31 1 Nov 5 Nov 7 Nov 8 Nov 12 Nov 14 Nov 15 19 21 22 26 28 29 Nov 3 Dec 5 Dec 6 Dec Thu Mon Wed Thu Mon Mon Wed Thu Mon Wed Thu Mon Wed Thu Mon Wed Thu Mon Wed Thu Mon Wed Thu Nov Nov Nov Nov Nov Nov Oct Oct Oct Oct Date 15 Oct 17 Oct Day Mon Wed Topics More wave equation solutions: The free particle in Cartesian coordinate, and the linear potential Quiz 8; The WKB approximation for bound states in one dimension Propagators, Green’s Functions, and the Schrödinger Wave Equation Propagators and the connection to path integrals and classical physics Quiz 9; Class cancelled: Instructor on travel Class cancelled: Instructor on travel Potentials and gauge transformations in quantum mechanics 6pm Makeup Class (JRSC 1C13): The Aharonov-Bohm Effect and magnetic monopoles Angular momentum as the generator of rotations in quantum mechanics Finite rotations in spin-1/2; Rotations through 2π Spin-1/2 using the Pauli two-component formalism Class cancelled: Instructor on travel Quiz 10; The groups SO(3), SU (2), and Euler rotations Density operators, ensembles, and quantum statistical mechanics Eigenvalues and eigenstates of general angular momentum from the commutation relations Quiz 11; Orbital angular momentum and rotations in three spatial dimensions Spherical harmonics Schrödinger’s Equation solutions for spherically symmetric potentials No Classes: Thanksgiving No Classes: Thanksgiving Examples: The free particle, the isotropic harmonic oscillator, and the Coulomb potential Addition of angular momenta Calculating Clebsch-Gordan coefficients Deterministic alternatives to quantum mechanics, and Bell’s innequality Vector operators Vector, tensor, and spherical tensor operators Matrix elements of tensor operators and the Wigner-Eckart Theorem Applications of the Wigner-Eckart Theorem 3.7 3.8 3.8, 3.9 3.10 3.11 3.11 3.11 3.11 3.6 3.6 3.7 3.3 3.4 3.5 2.7 2.7 3.1 3.2 3.2 2.5 2.6 2.6 Textbook 2.5 Day Date Topics Wed 23 Jan Symmetries, conservation laws, and degeneracies; SO(4) and Pauli’s solution to the hydrogen atom Continuous and discrete symmetries Thu 24 Jan Space-inversion (parity) symmetry and applications in nature Mon 28 Jan Lattice translation as a discrete symmetry and Bloch’s Theorem Wed 30 Jan Quiz 1; Time-reversal (“Reversal of motion”) symmetry: Formalism Thu 31 Jan Phenomenology of time-reversal symmetry Mon 4 Feb Time-independent, non-degenerate perturbation theory: Basic formalism Wed 6 Feb Quiz 2; Energies, states, and renormalization in time-independent perturbation theory; Basic examples Thu 7 Feb First order degenerate time-independent perturbation theory; The linear Stark effect Mon 11 Feb Second order degenerate time-independent perturbation theory Wed 13 Feb Quiz 3; Application to hydrogen-like atoms: The relativistic kinetic energy shift Thu 14 Feb Application to hydrogen-like atoms: The spin-orbit interaction, Lande’s rule, and the sodium atom Tue 19 Feb Application to hydrogen-like atoms: The Zeeman effect Wed 20 Feb Quiz 4; The variational method and its application to approximations Thu 21 Feb Time-dependent potentials: The interaction picture Mon 25 Feb Two-state problems with time-dependent potentials; Resonance phenomena Wed 27 Feb Quiz 5; The adiabatic approximation and Berry’s Phase Thu 28 Feb Time dependent perturbation theory and Fermi’s Golden Rule Mon 4 Mar Harmonic perturbations, and application to the classical radiation field Wed 6 Mar Quiz 6; Calculation of the photoelectric effect with the classical radiation field Thu 7 Mar Energy shift and decay width 11-15 March: Spring Break Modern Quantum Mechanics, Sakurai & Napolitano, Chapters 4 through 8 December 2, 2012 PHYS 6520/4520 Quantum Mechanics II (Spring 2013) 5.8 5.9 5.6 5.7 5.7, 5.8 5.4 5.5 5.5 5.3 5.3 5.3 5.1 5.2 Notes 4.4 4.4 5.1 Textbook 4.1 4.2 4.2 4.3 Day Date Topics Mon 18 Mar Scattering as a time-dependent perturbation: Transition rate, cross section, and the T -matrix Wed 20 Mar Quiz 7; Solving for the T -matrix; Mathematical interlude on poles and residues in complex analysis Thu 21 Mar Green’s Function for the Lippman-Schwinger Equation in coordinate space Mon 25 Mar The scattering amplitude and the optical theorem Wed 27 Mar Quiz 8; The Born approximation Thu 28 Mar Partial waves and the eikonal approximation Mon 1 Apr Low-energy scattering and the connection to bound states Wed 3 Apr Quiz 9; Resonance scattering Thu 4 Apr Identical particles and the symmetrization postulate Mon 8 Apr Two-electron systems and the helium atom Wed 10 Apr Quiz 10; Multiparticle states in second quantization Thu 11 Apr Example: The degenerate electron gas Mon 15 Apr Quantization of the electromagnetic field Wed 17 Apr Quiz 11; The Casimir effect Thu 18 Apr Fundamentals of quantum optics and “squeezed states” Mon 22 Apr Relativistic quantum mechanics and the Klein-Gordon Equation Wed 25 Apr Quiz 12; Fixing the problem with negative energies: The Klein-Gordon Field Thu 26 Apr The Dirac Equation and its elementary solutions Mon 29 Apr Negative energies and the electromagnetic interactions of spin-1/2 particles Wed 1 May Quiz 13; Angular momentum and parity symmetry in the Dirac Equation Thu 2 Apr Charge conjugation symmetry and time reversal symmetry in the Dirac Equation Mon 6 May The Dirac Equation and the hydrogen atom Wed 8 May Quiz 14; The relativistic hydrogen atom spectrum and the evidence for quantum electrodynamics 8.4 8.3 8.3 8.4 Notes 8.2 8.2 7.6 7.5, Notes 8.1 7.5 7.5 7.6 6.7 7.1, 7.2 7.3, 7.4 6.3 6.4, 6.5 6.6 6.1; Notes 6.2 6.2 Textbook 6.1