These lecture notes were prepared by Andrew Turner, who was the Teaching Assistant (TA) for the class.
| LEC # | LECTURE NOTES | TOPICS |
|---|---|---|
| 1 | Lecture 1 Notes (PDF) | A “Weird” Example in Quantum Mechanics, The Fundamental Postulates of Quantum Mechanics, Hilbert Spaces |
| 2 | Lecture 2 Notes (PDF) | Inner Products, Dual Space, Orthonormal Bases, Operators, Operators as Matrices in a Given Basis, Adjoint Operators, Operator Examples, Eigenstates and Eigenvalues |
| 3 | Lecture 3 Notes (PDF) | More on Matrix Representations, Unitary Transformations, Diagonalization of Hermitian Operators, Simultaneous Diagonalization, Measurement, Spin-1/2 Systems |
| 4 | Lecture 4 Notes (PDF) | Spin-1/2 Systems, The Stern-Gerloch Filter Revisited, Compatible and Incompatible Observables, The Generalized Uncertainty Relation, Position and Momentum |
| 5 | Lecture 5 Notes (PDF) | The Position Operator, Measurement of Position, Hilbert Spaces, Generalizing to Particles in Dimension d, The Momentum Operator, Momentum Basis, Normalization of Position and Momentum Eigenstates, Minimum Uncertainty States, Momentum and Translation |
| 6 | Lecture 6 Notes (PDF) | Solving Problems in Convenient Bases, Brief Aside on Classical Mechanics, The Heisenberg Picture, Energy Eigenstates, Example: Spin Precession in a Magnetic Field |
| 7 | Lecture 7 Notes (PDF) | Spin Precession in a Magnetic Field, Schrödinger Picture, Heisenberg Picture, Particle in a Potential, Example: Charged Particle in a Uniform Electric Field, Example: Simple Harmonic Oscillator |
| 8 | Lecture 8 Notes (PDF) | General Time Dependent Hamiltonians, Interaction Picture |
| 9 | Lecture 9 Notes (PDF) | Spin-1/2 in an AC Field, Resonant Drive, Off-Resonant Drive, Path Integral Formulation of Quantum Mechanics |
| 10 | Lecture 10 Notes (PDF) | Path Integral Formulation of Quantum Mechanics, The Propagator, Path Integrals |
| 11 | Lecture 11 Notes (PDF) | Path Integrals |
| 12 | Lecture 12 Notes (PDF) | Stationary Phase Approximation, Quantum Particles in Electromagnetic fields, Constant Potentials, Electromagnetic Fields, Gauge Invariance in Quantum Mechanics, Aharonov–Bohm Effect |
| 13 | Lecture 13 Notes (PDF) | Aharonov–Bohm Effect, Magnetic Monopoles |
| 14 | Lecture 14 Notes (PDF) | QM of a Charged Particle Moving in a Magnetic Monopole Field, Charged Particle in a Uniform Magnetic Field, Degeneracy |
| 15 | Lecture 15 Notes (PDF) | Charged Particle in a Uniform Magnetic Field, Quantum Entanglement |
| 16 | [Lecture 16 Notes not available] | |
| 17 | [Lecture 17 Notes not available] | |
| 18 | Lecture 18 Notes (PDF) | Symmetry Transformations, Continuous Symmetries and Conservation Laws, Time Translations, Rotations |
| 19 | Lecture 19 Notes (PDF) | Eigen system of Angular Momentum |
| 20 | Lecture 20 Notes (PDF) | Matrix Elements of Angular Momentum Operators, Rotation Groups |
| 21 | Lecture 21 Notes (PDF) | SO (3) versus SU (2), Addition of Angular Momentum, Discrete Symmetries |
| 22 | Lecture 22 Notes (PDF) | Some Standard Terminology, Wavefunctions Under Parity, Momentum and Angular Momentum, Selection Rules, Time Reversal and Spin |
| 23 | Lecture 23 Notes (PDF) | Consequences of Time Reversal Symmetry, Spinless Particles, No Conservation Law, Kramer’s Rule for Half-Integer Spin, Uses of Symmetry in Solving the Schrödinger Equation, Symmetric Double-Well Potential, 3D Particle in a Spherically Symmetric Potential, Approximation Methods, Time-Independent Perturbation Theory |
| 24 | Lecture 24 Notes (PDF) | Non-degenerate Time-Independent Perturbation Theory, The First-Order Energy Shift, The First-Order Correction to the Eigenstate, The Second-Order Energy Shift, Examples of Time-Independent Perturbation Theory, Spin in a Magnetic Field, The Quadratic Stark effect, Vander Waals Interaction |
| 25 | Lecture 25 Notes (PDF) | Degenerate Perturbation Theory, Linear Stark Effect, Time-Dependent Perturbation Theory, SHO in a Time-Dependent Electric Field, Second-Order Transition Amplitude |
| 26 | Lecture 26 Notes (PDF) | Harmonic Perturbations, The Photoelectric Effect |
