Topics discussed in this pdf include:
Introduction, Non-Technical Overview, Mathematical Background, The Foundations
of Quantum Theory, Continuous Quantum Systems, The Photoelectric Effect,
Motivation, Operations on Complex Numbers, Polar Coordinates and Complex Phases,
Complex Vector Spaces, Orthonormal Bases, Matrices and the Adjoint, The Outer
Product, The Completeness Relation, Representing Vectors in Different Bases,
Change of Basis, Multiplication and Inverse of Matrices, Matrices Inside Inner
Products, Eigenvalues and Eigenvectors, Hermitian Matrices, Unitary Matrices,
Normal Matrices, Representing Matrices in Different Bases, Diagonalizable
Matrices, Random Variables and Probability Distributions, Conditional
Probability, Expected Values, Standard Deviation, Dimensionless and Dimensionful
Constants, Hermitian Operators and Observables, Probability Amplitudes,
Superposition, Summary For Discrete Systems, The Pauli Matrices, Qubits, The
Meaning of Superposition, The Tensor Product, Vectors and Matrices in the
Composite Hilbert Space, Quantum Entanglement, The Bell States, Entanglement
Does Not Transmit Information, The Uncertainty Principle, Simultaneous
Diagonalization, Unitary Transformations and Evolution, Quantum Logic Gates,
Applications of the Measurement Axiom, Quantum Teleportation, Exponentials and
Logarithms, Matrix and Operator Exponentials, Hamiltonians and Energy, A Quick
Review of Classical Hamiltonian Mechanics, Canonical Quantization, The Classical
Harmonic Oscillator, Quantizing the Harmonic Oscillator, The Energy Eigenstates
of the Harmonic Oscillator, The Position Operator, Wavefunctions in the Position
Basis, The Momentum Operator, Quantum Interference, Separation of Variables.

**Author(s):** Barak Shoshany, Department of
Physics, University of Toronto

165**Pages**