| Week 1 | |
| Monday, August 27 | Introduction and Class Logistics Ch.1 Fundamental Concepts 1.1 The Stern-Gerlach Experiment |
| Wednesday, August 29 | 1.2 Kets, Bras, Inner product; 1.3 Base Kets 1.4 Measurements and Observables
HW 1 issued: Spin-1/2 States, due Wed Sep 12 |
| Friday, August 31 | 1.2 Outer product, Operators, Hermitian adjoint;
1.3 Matrix Representation
1.4 Spin 1/2 Systems, Pauli matrices, Quaternions Problem 1.9: Spin eigenstates for an arbitrary direction n |
| Week 2 | |
| Monday, September 3 | Labor Day, no lecture |
| Wednesday, September 5 | 1.4 (In)compatible Observables and (Non)commuting Operators;
Sequential Stern-Gerlach measurements; The Uncertainty Relation Prof. Yakovenko is away, substituted by Prof. Maissam Barkeshli |
| Friday, September 7 | 1.5 Change of Basis, Unitary Operators
1.6 Continuous Spectra; Position Eigenkets and Position Measurements; Translation operator; Generator of translations; Commutator with position operator; Generator of translations as momentum operator; Finite translations Prof. Yakovenko is away, substituted by Prof. Maissam Barkeshli |
| Week 3 | |
| Monday, September 10 | 1.7 Position-Space Wave Function; Momentum operator in position basis;
Momentum-space wave function; Fourier transform as the position-momentum basis change; Generalization to 3D HW 2 issued: Uncertainty Relation, due Mon Sep 17 |
| Wednesday, September 12 | 1.7 Coordinate operator in momentum basis;
A Gaussian wave packet as the state of minimal uncertainty (Problem 1.18) The uncertainty relation for position and momentum vs. time and frequency |
| Friday, September 14 | Ch.2 Quantum Dynamics 2.1 Time-Evolution Operator; Hamiltonian as the generator of time translation; Schodinger's equation; Energy Eigenkets; Spin precession; Neutrino oscillations |
| Week 4 | |
| Monday, September 17 | 2.1 Correlation Amplitude; Energy-Time Uncertainty Relation
2.2 The Schrodinger vs. the Heisenberg Picture HW 3 issued: Quantum dynamics, due Mon Sep 24 |
| Wednesday, September 19 | 2.2 Heisenberg Equations of Motion; Hamilton's Equations of Motion;
Poisson Brackets vs. the Commutator; Ehrenfest's Theorem; Virial Theorem HW 4 issued: Simple harmonic oscillator, due Wed Oct 3 |
| Friday, September 21 | 2.3 Simple Harmonic Oscillator; Creation and Annihilation Operators;
Energy spectrum; Wave Functions; Time Development of Harmonic Oscillator |
| Week 5 | |
| Monday, September 24 | 2.3 Coherent states of a harmonic oscillator: physical interpretation and over-completeness |
| Wednesday, September 26 | 2.4 Time-dependent and time-independent Schrodinger's equation;
Probability density and probability current; Equations for the amplitude and phase of the wave function; The Hamilton-Jacobi equation for the phase in the classical limit Prof. Yakovenko is away, substituted by Prof. Maissam Barkeshli |
| Friday, September 28 | 2.5 The Linear Potential; The semiclassical WKB Approximation; Connection at a turning point;
The Bohr-Sommerfeld quantization rule; Tunneling through a barrier Prof. Yakovenko is away, substituted by Prof. Maissam Barkeshli |
| Week 6 | |
| Monday, October 1 | 2.5 Number of quantum states within a phase-space volume; The energy density of states |
| Wednesday, October 3 | 2.4 Bound states of a semi-infinte square-well potential in 1D
HW 5 issued: Schrodinger's equation and WKB approximation, due Wed Oct 10 |
| Friday, October 5 | 2.6 Propagators and Feynman's Path Integrals;
Principle of minimal action in the classical limit;
Propagator of a free particle; Schrodinger's equation derived from path integral |
| Week 7 | |
| Monday, October 8 | Action as a function of the final coordinates; WKB derived from path integral;
Intro to functional integrals in the quantum field theory |
| Wednesday, October 10 | 2.7 Potentials and Gauge Transformations;
Constant potentials; Gravity in quantum mechanics;
Gauge Transformations in Electromagnetism |
| Friday, October 12 | 2.7 Gauge Transformations in Quantum Mechanics;
Action in the presence of electromagnetic field; Intro to non-Abelian gauge theories (quantum chromodynamics); The Aharonov-Bohm effect; Magnetic flux quantum HW 6 issued: Electromagnetic field and gauge transformations, due Mon Oct 22 |
| Week 8 | |
| Monday, October 15 | 2.7 Particle on a ring with a magnetic flux; Magnetic Monopole |
| Wednesday, October 17 | Midterm Exam in class covering Ch. 1 and Sections 2.1-2.5 of Ch. 2, open book |
| Friday, October 19 | 2.7 Motion in uniform magnetic and electric fields; Landau levels;
Degeneracy and filling factor; The quantum Hall effect; Corbino disk & Laughlin's argument: charge transfer vs. magnetic flux change |
| Week 9 | |
| Monday, October 22 | Vortices in superconductors
Ch.3 Theory of Angular Momentum Momentum, Hamiltonian, and Angular Momentum as the generators of space and time translation and space rotation HW 7 issued: Theory of Angular Momentum, due Mon Oct 29 |
| Wednesday, October 24 | 3.1 Rotations on a sphere; Commutation relation between
generators of rotations;
3x3 matrix representation of rotations of 3-vectors |
| Friday, October 26 | Spin 1 of a photon with circular polarization 3.2 Spin 1/2 systems;
Pauli 2-component formalism; Rotations in the 2-component formalism; Feynman's demonstration of 4pi periodicity; 4pi periodicity in neutron interferometry |
| Week 10 | |
| Monday, October 29 | 3.3 SO(3), SU(2), and Euler rotations
HW 8 issued: Theory of Angular Momentum, due Mon Nov 5 |
| Wednesday, October 31 | 3.5 Eigenvalues (j,m) and eigenstates of J^2 and J_z;
Commutation relations and ladder operators; Matrix elements of J+ and J- |
| Friday, November 2 | 3.5 Irreducible representations of the rotation operator
3.6 Orbital angular momentum as a generator of rotations; Transformation to spherical coordinates (Schwabl 5.1, 5.3); Spherical harmonics |
| Week 11 | |
| Monday, November 5 | 3.6 Spherical harmonics for l=1 in terms of x, y, z; Spherical Harmonics as
Rotation Matrices 3.7 Schrodinger's Equation for Central Potentials; Kinetic energy in terms of angular momentum HW 9 issued: Angular Momentum and Central Potential, due Mon Nov 12 |
| Wednesday, November 7 | 3.7 The Radial Equation; The spherical Bessel functions; The infinite spherical wall |
| Friday, November 9 | 3.7 The isotropic harmonic oscillator;
The Coulomb potential and the hydrogen atom
3.8 Addition of Angular Momenta; Addition of spins 1/2 and 1/2, singlet and triplet |
| Week 12 | |
| Monday, November 12 | 3.8 Hyperfine energy splitting of the hydrogen atom; Addition of j=1 and j=1;
Addition of orbital L and spin S angular momenta HW 10 issued: Addition of Angular Momenta, due Mon, Nov 19 |
| Wednesday, November 14 | 3.8 Addition of L and S=1/2; Spin-angular functions; Spin-orbital interaction;
Fine structure (splitting) of energy levels in j; Exchange symmetry for indistinguishable particles; Exchange interaction between electrons |
| Friday, November 16 | 3.8 Recursion relations for the Clebsch-Gordan coefficients;
3.9 Schwinger's Oscillator Model of Angular Momentum; Explicit Formula for Rotation Matrices |
| Week 13 | |
| Monday, November 19 | 3.8 Clebsch-Gordan Coefficients and Rotation Matrices;
3.11 Tensor Operators; Irreducible Tensors HW 11 issued: Spherical Tensors, due Mon, Dec 3 |
| Wednesday, November 21 | Thanksgiving Holiday, no lecture |
| Friday, November 23 | Thanksgiving Holiday, no lecture |
| Week 14 | |
| Monday, November 26 | 3.11 Vector Operator; Cartesian vs. Spherical Tensors |
| Wednesday, November 28 | 3.11 Product of Tensors; Gravitational wave of the rank-2 symmetric
metric tensor; Quadrupolar polarization and spin 2 of gravitational waves; Matrix Elements of Tensor Operators; Wigner-Eckart Theorem;Projection Theorem |
| Friday, November 30 | Ch.4 Symmetry in Quantum Mechanics
4.1 Symmetries, Conservations Laws, and Degeneracies, in classical and quantum mechanics; SO(4) Symmetry of the Coulomb Potential; 4.2 Parity or Space Inversion, Polar and axial vectors, Pseudoscalars; Wave Functions Under Parity; Symmetric Double-Well Potential; NH3 molecule |
| Week 15 | |
| Monday, December 3 | 4.2 Spin-orbit interaction with and without inversion symmetry;
Spherical functions Ylm under parity; Parity Selection Rule; Electric dipole and magnetic dipole transitions HW 12 issued: Symmetry, due Mon Dec 10 |
| Wednesday, December 5 | Non-centrosymmetric, polar, and chiral (optical isomers) molecules, monochirality in biology;
Parity Nonconservation in Weak Interactions; Helicity of neutrinos; CP symmetry |
| Friday, December 7 | 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 10
update point |
4.4 Time Reversal for Spin 1/2; Kramers Degeneracy;
Coupling to Electric and Magnetic Fields
3.10 Entangled States 3.4 Density Operator; Pure versus Mixed Ensembles Home Reading: 4.3 Lattice Translation as a Discrete Symmetry; Tight-binding approximation |
| Final Exam | |
| Tuesday, December 18 | 8-10 am, ATL 1113; Chapters 3 and 4; open book. |
Last updated December 10, 2018