What you will learn
By taking this course, you will learn about:
 Planck’s constraint in action
 Schoroe dinger equation
 Energy and time
 Waves
 Strings and Sounds
 Oscillator
 Atoms and Hydrogen atom
 Angular momentum etc.
Contents
Module 1 INTRODUCTION
Module 2 PLANCK’S CONSTANT IN ACTION
Module 3 THE SCHROÈ DINGER EQUATION
Module 4 POSITION AND MOMENTUM
Module 5 ENERGY AND TIME
Module 6 SQUARE WELLS AND BARRIERS
Module 7 THE HARMONIC OSCILLATOR
Module 8 OBSERVABLES AND OPERATORS
Module 9 ANGULAR MOMENTUM
Module 10 THE HYDROGEN ATOM
Module 11 IDENTICAL PARTICLES
ATOMS
Topics Covered
INTRODUCTION Lecturer Introduction
Importance of this course
What you will learn in this course
PLANCK’S CONSTANT IN ACTION
• Photons
• De Broglie Waves
• Atoms
• Measurement
a. The uncertainty principle
b. Measurement and wave±particle duality
c. Measurement and non-locality
THE SCHROÈ DINGER EQUATION • Waves
a. Sinusoidal waves
b. Linear superpositions of sinusoidal waves
c. Dispersive and non-dispersive waves

• Particle Wave Equations
a. A wave equation for a free particle
b. Wave equation for a particle in a potential energy field
POSITION AND MOMENTUM • Probability
a. Discrete random variables
b. Continuous random variables

• Position Probabilities
a. Two-slit interference
b. The Born interpretation of the wave function

• Momentum Probabilities
• A Particle in a Box I
• Expectation Values
a. Operators
b. Uncertainties

• Quantum States
ENERGY AND TIME • The Hamiltonian Operator
• Normal Modes of a String
• States of Certain Energy
• A Particle in a Box II
a. A one-dimensional box
b. A three-dimensional box

• States of Uncertain Energy
a. Basis functions
b. Energy probability amplitudes

• Time Dependence
SQUARE WELLS AND BARRIERS • Bound and Unbound States
a. Bound states 85
b. Unbound states 88
c. General implications 93

• Barrier Penetration
a. Stationary state analysis of reflection and transmission
b. Tunnelling through wide barriers
c. Tunnelling electrons
d. Tunnelling protons
THE HARMONIC OSCILLATOR • The Classical Oscillator
• The Quantum Oscillator
• Quantum States
a. Stationary states
b. Non-stationary states
• Diatomic Molecules
• Three-dimensional Oscillators
• The Oscillator Eigenvalue Problem
a. The ground state
b. Excited states
c. Is E0 really the lowest energy?
d. Mathematical properties of the oscillator eigenfunctions
OBSERVABLES AND OPERATORS • Essential Properties
• Position and Momentum
a. Eigenfunctions for position
b. Eigenfunctions for momentum
c. Delta function normalization

• Compatible Observables
• Commutators
a. A particle in one dimension
b. A particle in three dimensions

• Constants of Motion
ANGULAR MOMENTUM • Angular Momentum Basics
• Magnetic Moments
a. Classical magnets
b. Quantum magnets
c. Magnetic energies and the Stern±Gerlach experiment

• Orbital Angular Momentum
a. Classical orbital angular momentum 163
b. Quantum orbital angular momentum 164
c. Angular shape of wave functions 164
d. Spherical harmonics 169
e. Linear superposition 171
THE HYDROGEN ATOM • Central Potentials
a. Classical mechanics of a particle in a central potential
b. Quantum mechanics of a particle in a central potential
• Quantum Mechanics of the Hydrogen Atom
a. Energy levels and eigenfunctions
• Sizes and Shapes