Quantum Mechanics
Origins of Quantum Mechanics
A Brief History of Quantum Mechanics
Blackbody Radiation
The Photoelectric Effect
The Compton Effect
de Broglie Matter Waves
Wave-Particle Duality
Probability and Uncertainty in Quantum Mechanics
Atomic Transitions and Spectroscopy
Wave Packets
Summary
Mathematical Tools
Hilbert Space
Dirac Notation
Linear Operators
Basic Properties of Linear Operators
Adjoints and Hermitian Operators
Commutators and Uncertainty Relations
Functions, Inverses, and Unitary Operators
Eigenvalues and Eigenvectors
Representing Operators in Discrete Bases
Fourier Series and Fourier Transforms
Continuous Basis Representations
Summary
Postulates of Quantum Mechanics
Summary of the Basic Postulates
The State Space of a Quantum System
The Schrödinger Equation
Observables as Operators
The Infamous Measurement Postulates
Compatible and Incompatible Observables
The Heisenberg Picture and Conservation Laws
Solving the Schrödinger Equation for Degenerate Hamiltonians
Summary
One Dimensional Problems
The Free Particle
The Infinite Square Well Potential
General Considerations
The Potential Step
The Potential Barrier
The Delta Function Potential
The Finite Square Well Potential
The Harmonic Oscillator
Summary
Angular Momentum
Three Dimensional Problems
The Variational Principle
The Variational Principle