The Mathematics of Chance
- Probability Distributions for discrete and continuous systems.
- Combined probabilities and averages
- The effect of measurement of probabilities
Introduction to Quantum Mechanics
- Review of Classical Mechanics – Postulates and Newton’s Equations of Motion
- The birth of quantum theory, historical background and the failures of classical mechanics.
- Blackbody radiation
- The photoelectric effect
- Atomic Spectra
- Bohr theory of the atom.
- Advent of wave theory
- Quantum mathematical preview.
- Complex Conjugates and absolute squares.
- Eigenvalues and operators algebra.
- Hermetian operators and commutators.
- Postulates of quantum mechanics.
- Heisenberg Uncertainty Principle
- The Schrodinger wave equation.
- Time dependent
- Time independent.
Quantum Mechanical Treatment of Translational, Rotational and Vibrational Motions
- Translational Motion
- The 1-D and 3-D Free particle
- Particle in an infinite well.
- Superposition of states
- Tunnelling
- Rotational Motion
- Center-of-Mass coordinate system and internal motion.
- The rigid rotator quantum system.
- Wave functions and angular momentum.
- Rotation of polyatomic molecules
- Vibrational Motion
- The classical vibrator – Harmonic Oscillator
- Quantum mechanical harmonic oscillator
- Anharmonic oscillator and anharmonic effects.
- Coupling of internal motions
Electronic Structure of Atoms
- Introduction to atomic unit system.
- The one-electron hydrogen-like atom
- Wave functions and energy levels
- Atomic spectra
- Average values and the Virial Theorem
- Quantum spin
- Stern and Gerlach experimental discovery of spin
- P.M Dirac and the development of relativistic quantum mechanics
- Addition of angular momentum
- Magnetic field effects on orbital and spin angular momentum.
- Term Symbols and Spin-Orbit Coupling
- Many-electron Atoms
- General form of the Hamiltonian and the coupled motion problem.
- Helium atom.
- L-S coupling and many electron term symbols.
- Hunds Rules
Approximation Methods
- Perturbation Theory
- Application to the helium atom
- Variational Theory
- Simple variational theory
- Linear Variational Theory and the development of the secular determinant.
Molecular Structure and Bonding
- The hydrogen molecular ion and the origin of the chemical bond.
- Valence Bond Theory and Molecular Orbital Theory.
- GAUSSIAN and ab initio computations.
- SCF calculations using LCAO-MO.
- Interpretation of output.
- Qualitative treatment of many electron molecules.
- CI, MP MNDO and DFT calculations
Spectroscopy
- Origin of absorption spectra
- Transition probabilities
- Selection rules
- Bandwidths
- Absorption band Intensities
- Rotational Spectroscopy
- Diatomic molecules.
- Polyatomic molecules
- Introduction to FFT
- Vibrational Spectroscopy
- Diatomic molecules
- Polyatomic molecules
Statistical Mechanics
- Microstates and quantum state distributions.
- The molecular partition function
- Separation of motions into individual partition functions
- Translational partition function
- Rotational partition function
- Vibrational partition function
- Electronic and nuclear partition functions
- Canonical partition function
- Computation of Thermodynamic Values
- Gibbs Free Energy and the Equilibrium Constant.
