Quantum Mechanics

Notes from Dr John Marangros' Lectures

Part I
Quantum Mechanics 1

• Lecture 1 - Particle-Wave Duality
  • The Photoelectric Effect (waves behaving like particles)
  • Electron Diffraction (particles behaving like waves)
• Lecture 2 - Uncertainity and Quantum Waves
  • Properties of Classical Waves
  • Diffraction of a Quantum Wave
  • Wave Function of a Matter Wave
• Lecture 3 - Superposition and Non-Classical Physics
  • Two Slit Interference
  • Non-Classical Physics

Part II
Basic Formalism of Quantum Mechanics

• Lecture 4 - Postulates of Quantum Mechanics
  • Postulate A - Dynamic Variables (Observerables)
  • Postulate B - Wavefunctions
  • Postulate C - Superpositions
  • Postulate D - Time Dependence
• Lecture 5 - Operators
  • Properties of Operators
  • Construction of Operators
  • Operators and Measurements
• Lecture 6 - States and Wave Functions
  • States of a Quantum System
  • Wavefunctions
• Lecture 7 - Energy Eigenstates and Eigenvalues
  • Time Dependence
  • An Energy Operator in Spatial Coordinates
• Lecture 8 - Overlap Integrals, Expectation Values and Superpositions
  • Superpositions
  • Overlap Integral
  • Expectation Values
• Lecture 9 - Compatibility of Observables and Communtation Relations
  • Compatible and Incompatible Observables
  • Commutators
  • Some Important Communtation Relations
• Summary 1
  • General Meanings
  • Operators
  • Generic Hermition Functions

Part III
One Dimensional Systems

• Lecture 10 - The Infinite Square Well
  • Free Particle
  • Infinite Square Well
• Lecture 11 - Finite Square Well
  • Characteristics of Well
  • Form of Energy Eigenfunctions
  • Determination of Energy Eigenvalues
  • Graphically Obtained Solution
• Lecture 12 - Potential Steps, Barriers and Tunneling
  • Potential Step
  • Barriers and Tunneling
• Lecture 13 - Quantum Harmonic Oscillator
  • Harmonic Oscillator Potential
  • Quantum Harmonic Oscillator
  • Ladder Operators
• Lecture 14 - Ladder Operators and Solution of the Quantum Harmonic Oscillator
  • Action of (matrix)A and (matrix)A(dagger)
  • Energy Eigenvalues of the Quantum Oscillator
  • Eigenstates of the Harmonic Oscillator
• Lecture 15 - Eigenstates of the Quantum Harmonic Oscillator - Continued
  • Hermite Polynominals
  • Comparision To The Classical Harmonic Oscillator System
  • Vibrational States of Diatomic Molecules
  • The Vibrational Modes of a Crystal Lattice
• Lecture 16 - Review of The Quantum Mechanics of One Dimensional Systems
  • Symmetry of Wavefunctions
  • Uncertainity Relations in Quantum Wells
  • Dynamics of Superposition of Energy Eigenstates

Part IV
Three Dimensional Systems and Angular Momentum

• Lecture 17 - Three Dimensional Systems
  • Introduction
  • Three Dimensional Hamiltonian
  • Parity
  • Angular Momentum
• Lecture 18 - Operators for Angular Momentum and Their Commutation Relations
  • Angular Momentum Operator
  • Compatibility of Angular Momentum Operators
  • Communtation Relations Between Angular Momentum Operators
• Lecture 19 - Eigenfunctions of Angular Momentum
  • Angular Momentum Eigenvalue Equation
  • hat(L)z Eigenstates and Eigenvalues
  • Spherical Harmonics
• Lecture 20 - Angular Momentum in Atoms and Molecules
  • Diatomic Molecules
  • Central Potentials - Atoms
• Lecture 21 - Spin
  • The Nature and Discovery of Spin
  • The Interaction of Angular Momentum With a Magnetic Field
  • Stern-Gerlach Experiment (1925)
  • Spin States and Operators

Part V
Further Quantum Theory

• Lecture 22 - Temporal Evolution of Quantum Systems
  • Evolution of Energy Eigenstates
  • Evolution of an Expectation Value
  • Evolution in a Time Varying Potential
• Lecture 23 - Temporal Evolution in a Two Level System
  • Transitions Between Eigenstates
  • Two Level Systems
  • Resonant Interaction
• Lecture 24 - Perturbation Theory
  • The Quantum Mechanics of Real Systems
  • Perturbation Theory
• Lecture 25 - Examples of Perturbation Theory
  • Non-Degenerate Perturbation Theory
  • Degenerate Perturbation Theory - A Hydrogen Atom in an Electric Field
• Lecture 26 - Systems With Several Particles
  • Multiple Particle Wavefunctions
  • Non-Interacting Particles
  • Identical Particles

This document was translated from L^AT_EX by H^EV^EA and H^AC^HA.