1 Introduction
 1.1 Black-body radiation
 1.2 Photo-electric effect
 1.3 Hydrogen atom
 1.4 Wave particle duality
 1.5 Uncertainty
 1.6 Tunneling
2 Concepts from classical mechanics
 2.1 Conservative fields
 2.2 Energy function
 2.3 Simple example
3 The Schrödinger equation
 3.1 The state of a quantum system
 3.2 Operators
 3.3 Analysis of the wave equation
4 Bound states of the square well
 4.1 {B}_{2} = 0
 4.2 {A}_{2} = 0
 4.3 Some consequences
 4.4 Lessons from the square well
 4.5 A physical system (approximately) described by a square well
5 Infinite well
 5.1 Zero of energy is arbitrary
 5.2 Solution
6 Scattering from potential steps and square barriers, etc.
 6.1 Non-normalisable wave functions
 6.2 Potential step
 6.3 Square barrier
7 The Harmonic oscillator
 7.1 Dimensionless coordinates
 7.2 Behaviour for large |y|
 7.3 Taylor series solution
 7.4 A few solutions
 7.5 Quantum-Classical Correspondence
8 The formalism underlying QM
 8.1 Key postulates
  8.1.1 Wavefunction
  8.1.2 Observables
  8.1.3 Hermitean operators
  8.1.4 Eigenvalues of Hermitean operators
  8.1.5 Outcome of a single experiment
  8.1.6 Eigenfunctions of ˆx
  8.1.7 Eigenfunctions of ˆp
 8.2 Expectation value of {ˆx}^{2} and {ˆp}^{2} for the harmonic oscillator
 8.3 The measurement process
  8.3.1 Repeated measurements
9 Ladder operators
 9.1 Harmonic oscillators
 9.2 The operators ˆa and {ˆa}^{†}.
 9.3 Eigenfunctions of ˆH through ladder operations
 9.4 Normalisation and Hermitean conjugates
10 Time dependent wave functions
 10.1 correspondence between time-dependent and time-independent solutions
 10.2 Superposition of time-dependent solutions
 10.3 Completeness and time-dependence
 10.4 Simple example
 10.5 Wave packets (states of minimal uncertainty)
 10.6 computer demonstration
11 3D Schrödinger equation
 11.1 The momentum operator as a vector
 11.2 Spherical coordinates
 11.3 Solutions independent of θ and φ
 11.4 The hydrogen atom
 11.5 Now where does the probability peak?
 11.6 Spherical harmonics
 11.7 General solutions