1. The Emergence of Quantum Physics
• Blackbody Radiation
• The Bohr Atom (the Correspondence Principle)
2. Wave Particle Duality, Probability and the Schrödinger Equation (Wave Mechanics)
• Classical vs. Wave mechanics (duality of particle and wave)
• The Probability Interpretation of the Wave Function
• The Schrödinger equation
• Probability
• Normalization
• Momentum
• Uncertainty Principle
• Wave Function in Momentum Space
3. Time-independent Schrödinger Equation (1D cases)
• Stationary States The free particle
• The free particle
• The Infinite Square Well Potential
• The Harmonic Oscillator
• The Delta-function potential and its related problems
• Finite Square Well Potential: Potential Well, Potential step, and Potential barrier
4. Formalism for Quantum Mechanics
• The Stern-Gerlach experiment
• Quantum states: the space of states; kets and its dual space-bras; inner product.
• Operators, Eigenstates, Hermitian operators.
• Base kets, Completeness, and Expansion in Eigenstates.
• Matrix Representation.
• Change of Basis
• Postulates of Quantum Mechanics.
• Measurements, Observables, Commuting Operator, Compatible Observables, Noncommuting Operators, Incompatible Observables.
• Uncertainty Relations.
• Position, Momentum, and Translation.
• Wave Functions in Position and Momentum Space
• Application to Harmonic Oscillators
5. Quantum Dynamics
• Time Dependence and Classical limit
• Time Evolution Operator
• Energy-time Uncertainly Relation
• The Schrodinger Picture versus Heisenberg Picture
• The Evolution of Momentum and Position in Harmonic Oscillator
• Coherent States of Harmonic Oscillator
6. Spin and addition of angular momentum
• Spin: from Classical to Quantum Mechanics
• Eigenstates of spin 1/2
• Spin Precession and NMR
• Paramagnetic Resonance
• Addition of Angular Momentum