| Week 1 | |
| Monday, August 29 | Introductory Lecture |
| Wednesday, August 31 | Ch.1 Fundamental Concepts 1.1 The Stern-Gerlach Experiment |
| Friday, September 2 | 1.2 Kets, Bras, and Operators 1.3 Base Kets and Matrix Representation 1.4 Measurements |
| Week 2 | |
| Monday, September 5 | Labor Day, no lecture |
| Wednesday, September 7 | Spin 1/2 Systems, Pauli matrices |
| Friday, September 9 | Problem 1.9: Spin eigenstates for an arbitrary direction n 1.5 Change of Basis, Unitary Operators HW 1 issued: Spin 1/2 states |
| Week 3 | |
| Monday, September 12 | Problem 1.3: Rotation operator for spin 1/2; Quaternions |
| Wednesday, September 14 | 1.5 Trace of operators; 1.4 The Uncertainty Relation |
| Friday, September 16 | Problem 1.18: The state of minimal uncertainty 1.6 Continuous Spectra; Position Eigenkets and Position Measurements; Translation Operator; Momentum as a Generator of Translations 1.7 Position-Space Wave Function HW 2 issued: Uncertainty relations |
| Week 4 | |
| Monday, September 19 | Momentum operator in position basis, Momentum-space wave function,
Fourier transform as the position-momentum basis change, Coordinate operator in momentum basis, Generalization to 3D |
| Wednesday, September 21 | The uncertainty relation for position and momentum,
a Gaussian wave packet as the minimal uncertainty state, The uncertainty relation for time and frequency |
| Friday, September 23 | Ch.2 Quantum Dynamics 2.1 Time-evolution and the Schodinger equation, Energy eigenkets, Spin precession, Neutrino oscillations, Energy-time uncertainty relation HW 3 issued: Quantum dynamics |
| Week 5 | |
| Monday, September 26 | 2.2 The Schrodinger vs. the Heisenberg Picture, Heisenberg Equations of Motion |
| Wednesday, September 28 | Classical Hamilton's Equations of Motion,
Poisson Brackets vs. the Commutator,
Ehrenfest's Theorem, Virial Theorem |
| Friday, September 30 | 2.3 Simple Harmonic Oscillator, Creation and Annihilation Operators,
Time Dynamics, Coherent States HW 4 issued: Simple harmonic oscillator |
| Week 6 | |
| Monday, October 3 | Over-completeness and physical interpretation of coherent states;
2.4 Schrodinger's wave equation; Probability density and probability current |
| Wednesday, October 5 | Equations for the amplitude and phase of the wave function;
The Hamilton-Jacobi equation for the phase in the classical limit; An excursion into quantum field theory |
| Friday, October 7 | 2.5 The WKB (semiclassical) Approximation;
Tunneling through a barrier;
The Bohr-Sommerfeld quantization rule HW 5 issued: The WKB approximation |
| Week 7 | |
| Monday, October 10 | Number of quantum states within phase-space volume;
The energy density of states |
| Wednesday, October 12 | Stationary-phase approximation for a linear potential;
The WKB connection formulas around the turning point |
| Friday, October 14 | 2.6 Propagators and Feynman Path Integrals |
| Week 8 | |
| Monday, October 17 | 2.7 Potentials and Gauge Transformations;
Constant potentials;
Gravity in quantum mechanics; Gauge transformations in electromagnetism |
| Wednesday, October 19 | Intro to non-Abelian gauge theories (quantum chromodynamics)
The Aharonov-Bohm effect HW 6 issued: Electromagnetic field and gauge transformations |
| Friday, October 21 | Magnetic flux quantum; Magnetic Monopole; Vortices in superconductors
Motion in uniform magnetic and electric fields |
| Week 9 | |
| Monday, October 24 | Landau levels; Degeneracy and filling factor; The quantum Hall effect |
| Wednesday, October 26 | Ch.3 Theory of Angular Momentum
Action as a function of the final coordinates; Linear momentum, Hamiltonian, and angular momentum as the generators of translation in space and time, and space rotation |
| Friday, October 28 | 3.1 Rotations on sphere; The general commutation relation between
generators of rotations;
3x3 matrix representation of rotations of 3-vectors; Spin 1 of a photon with circular polarization HW 7 issued: Theory of Angular Momentum |
| Week 10 | |
| Monday, October 31 | 3.2 Spin 1/2 systems; Pauli 2-component formalism;
Rotations in the 2-component formalism;
Spin precession revisited; Neutron interferometry experiment to confirm 4pi periodicity; Feynman's demonstration of 4pi periodicity |
| Wednesday, November 2 | 3.3 SO(3), SU(2), and Euler rotations |
| Friday, November 4 | Midterm Exam in class covering
Chapters 1 and 2 open book, proctored by Prof. Jay Sau.
Prof. Yakovenko is away to Boston. |
| Week 11 | |
| Monday, November 7 | 3.5 Eigenvalues (j,m) and eigenstates of angular momentum
operators J^2 and J_z;
Commutation relations and ladder operators; Matrix elements of J+ and J-; Irreducible representations of the rotation operator |
| Wednesday, November 9 | 3.6 Orbital angular momentum as rotation generator
HW 8 issued: Theory of Angular Momentum |
| Friday, November 11 | 3.6 Spherical harmonics, as rotation matrices |
| Week 12 | |
| Monday, November 14 | 3.7 Schrodinger's Equation for Central Potentials;
The radial equation;
The free particle, the spherical Bessel functions, and the infinite spherical wall |
| Wednesday, November 16 | The isotropic harmonic oscillator; The Coulomb potential and the hydrogen atom |
| Friday, November 18 | 3.8 Addition of Angular Momenta;
Addition of spins 1/2 and 1/2, singlet and triplet, hyperfine energy splitting of the hydrogen atom; Addition of j=1 and j=1 |
| Week 13 | |
| Monday, November 21 | Addition of orbital L and spin S angular momenta;
Recursion relations for the Clebsch-Gordan coefficients HW 9 issued: Addition of Angular Momentum |
| Wednesday, November 23 | Thanksgiving Holiday, no lecture |
| Friday, November 25 | Thanksgiving Holiday, no lecture |
| Week 14 | |
| Monday, November 28 | 3.9 Schwinger's Oscillator Model of Angular Momentum
Explicit Formula for Rotation Matrices |
| Wednesday, November 30 | 3.11 Tensor Operators
Vector Operator; Cartesian Tensors vs. Irreducible Spherical Tensors |
| Friday, December 2 | Product of Tensors; Matrix Elements of Tensor Operators;
The Wigner-Eckart Theorem
HW 10 issued: Spherical Tensors |
| Week 15 | |
| Monday, December 5 | Ch.4 Symmetry in Quantum Mechanics
4.1 Symmetries, Conservations Laws, and Degeneracies, in classical and quantum mechanics; 4.2 Parity or Space Inversion, in geometry |
| Wednesday, December 7 | Transformation of the coordinate, momentum, and angular momentum
operators upon time reversal;
Polar and axial vectors, pseudoscalars; Wave Functions (of angular momentum) Under Parity; Symmetric Double-Well Potential, NH3 molecule; Non-centrosymmetric, chiral (optical isomers), and polar molecules |
| Friday, December 9 | Parity Selection Rule; Parity Nonconservation in Weak Interactions;
Helicity of Neutrinos;
4.4 The Time-Reversal Symmetry; Antiunitary Operators; Transformation of wave functions and the coordinate, momentum, and angular momentum operators upon time reversal |
| Week 16 | |
| Monday, December 12
update point |
Time Reversal for a Spin 1/2 System; Interaction with Electric
and Magnetic Fields; Kramers Degeneracy;
4.3 Lattice Translation as a Discrete Symmetry; Tight-binding approximation; Ring molecules |
| Final Exam | |
| Tuesday, December 20 | 8-10 am, Room 1204; Open book exam - you can use the textbook and your notes. |
Last updated December 12, 2016