8.321 | Fall 2017 | Graduate

Quantum Theory I

Lecture Notes

These lecture notes were prepared by Andrew Turner, who was the Teaching Assistant (TA) for the class.

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

Course Info

As Taught In
Fall 2017
Learning Resource Types
Problem Sets
Lecture Notes