Quantum Theory I: Lecture Notes

Sep. 6, 2017
A ``Weird'' Example in Quantum Mechanics
The Fundamental Postulates of Quantum Mechanics
Mathematical Preliminaries
Hilbert Spaces
Sep. 11, 2017
More Relevant Math
Inner Products
Dual Space
Orthonormal Bases
Operators
Operators as Matrices in a Given Basis
Adjoint Operators
Operator Examples
Eigenstates and Eigenvalues
Sep. 13, 2017
Even More Math
More on Matrix Representations
Unitary Transformations
Diagonalization of Hermitian Operators
Simultaneous Diagonalization
Measurement
Comments
Spin-12 Systems
Sep. 18, 2017
Measurement
Spin-12 Systems
The Stern–Gerloch Filter Revisited
Compatible and Incompatible Observables
The Generalized Uncertainty Relation
Position and Momentum
Sep. 20, 2017
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
The Uncertainty Principle
Minimum Uncertainty States
Momentum and Translation
Sep. 25, 2017
Solving Problems in Convenient Bases
Quantum Dynamics
Brief Aside on Classical Mechanics
The Heisenberg Picture
Energy Eigenstates
Example: Spin Precession In a Magnetic Field
Sep. 27, 2017
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
Oct. 2, 2017
General Time Dependent Hamiltonians
Interaction Picture
Oct. 4, 2017
Spin-12 in an AC Field
Resonant Drive
Off-Resonant Drive
Path Integral Formulation of Quantum Mechanics
Oct. 11, 2017
Path Integral Formulation of Quantum Mechanics
The Propagator
Path Integrals
Oct. 16, 2017
Path Integrals
Technical Details
Oct. 23, 2017
Stationary Phase Approximation
Quantum Particles in Electromagnetic fields
Constant Potentials
Electromagnetic Fields
Gauge Invariance in Quantum Mechanics
Aharonov–Bohm Effect
Oct. 25, 2017
Aharonov–Bohm Effect
Magnetic Monopoles
Oct. 30, 2017
Magnetic Monopoles
QM of a Charged Particle Moving in a Magnetic Monopole Field
Charged Particle in a Uniform Magnetic Field
Degeneracy
Nov. 1, 2017
Charged Particle in a Uniform Magnetic Field
Composite Systems
Quantum Entanglement
Nov. 13, 2017
Symmetries in Quantum Mechanics
Symmetry Transformations
Continuous Symmetries and Conservation Laws
Translations
Time Translations
Rotations
Nov. 15, 2017
Rotations
Eigensystem of Angular Momentum
Nov. 20, 2017
Matrix Elements of Angular Momentum Operators
Rotation Groups
Nov. 22, 2017
`39`42`"613A``45`47`"603ASO(3) versus `39`42`"613A``45`47`"603ASU(2)
Addition of Angular Momentum
Discrete Symmetries
Nov. 27, 2017
Parity
Some Standard Terminology
Wavefunctions Under Parity
Momentum and Angular Momentum
Selection Rules
Time Reversal
Time Reversal and Spin
Nov. 29, 2017
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
Dec. 4, 2017
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
Van der Waals Interaction
Dec. 6, 2017
Degenerate Perturbation Theory
Linear Stark Effect
Time-Dependent Perturbation Theory
SHO in a Time-Dependent Electric Field
Second-Order Transition Amplitude
Dec. 11, 2017
Harmonic Perturbations
The Photoelectric Effect