PHYS3022 Applied Quantum Mechanics (2018-2019 Term 2)
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PHYS3022 Applied Quantum Mechanics (2018-2019 Term 2)
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Class Notes [Front Matter]
Course Policies, Assessment Scheme, Necessary condition for a passing grade, Exercise Classes and Assignments, TA contacts
PHYS3022 - Course Time Table - Lectures Hours - Exercise Classes - TA consultation hours and contacts
PHYS3022 - Book List (Quantum Physics and Quantum Mechanics Books, Books on Atoms, Molecules, Nuclei, and Math Skills)
PHYS3022 - Course Learning Outcomes
Chapter 0 - Overview, coverage of course, and assumed knowledge

Class Notes [Self-Revision on Essential QM covered in PHYS3021]
Self-Revision Part 1 - The Schrodinger Equations TDSE and TISE and Types of Related Problems
Self-Revision Part 2 - Summary of Results of Standard QM TISE Problems
Self-Revision Part 3 - Spin of Electron

Class Notes [Methods (mostly approximations) in QM]
AM Part 1 - Motivations - Many QM Problems cannot be solved analytically and ask for approximations
AM Part 2 - An Exact Approach - Turning TISE into a huge matrix problem
AM Part 3 - Variational Method [Revised] (What it says, the theorem, varying trial wavefunctions, examples, trial wavefunction in linear combination form)
AM Part 4 - Time-independent Non-degenerate Perturbation Theory - Formalism and physical sense of results
AM Part 5 - An example of perturbation calculations and suggested exercises
AM Part 6 - Perturbation Results Made Simple by Matrix Point of View, Degenerate Perturbation Theory is a by-product - Summary

Class Notes [Physics of Atoms]
AP I Part 1 - What data said - Normal Zeeman Effect - Anomalous Zeeman Effect and Fine Structure ask for more physics
AP I Part 2 - Angular Momentum in QM - Orbital AM - Spin AM - Adding two momenta
AP I Part 3 - Spin-Orbit Interaction - First Order Calculation - Relativistic Correction - Term Symbols - What Data say - Lamb Shift
AP I Part 4 - Zeeman Effect Revisited - Hamiltonian with Hso and Zeeman - Strong field and Weak field cases - Anomalous Zeeman effect explained
AP I Part 5 - Hyperfine Structure - 21 cm line of hydrogen in astronomy - 500m aperture spherical radio telescope (FAST)
AP II Part 1 - Big Picture 1 - Multi-electron Atoms are Difficult Many-body problems - Find a way out
Lead Sheet - Hydrogen atom and Hydrogenic systems
AP II Part 2 - Helium Atom - Perturbation - Variational Method - Effective PE term in single-electron approximation
AP II Part 3 - Big Picture 2 - Independent Particle Approximation and Energies of single-electron states
AP II Appendix A - The Atomic Units make equations and results look simpler
AP II Appendix B - Single-electron Atomic Orbitals are results of Self-Consistent Field Calculations
AP II Part 4 - Antisymmetric Many-Electron Wavefunction and Pauli Exclusion Principle
AP II Part 5 - Helium 1st Excited State - Exchange Coulomb Integral and the Origin of Ferromagnetism
AP II Part 6 - The Periodic Table
AP II Part 7 - Quantum Entanglement

Class Notes [Atomic transitions, Light-Matter Interaction and Approximation (cont
LMI-I Part 1 Phenomena of Light-Matter interaction - QM is OK - Hand waving theory gives key result
LMI-I Part 2 Electric-dipole mechanism, Time dependent Perturbation term, and Time-dependent Perturbation Theory (set up)
LMI-I Part 3 Stimulated absorption and emission - Energy must match and Selection Rules - all emerged from theory
LMI-II Part 1 Transition rates for stimulated absorption and stimulated emission
LMI-II Part 2 Einstein (1917) A and B coefficients and Relation between A and B
LMI-II Part 3 Spontaneous emission transition rate from QM and Life time of an excited state
LMI-II Part 4 Natural Broadening - Lorzentian line-shape function - FWHM and life time - Energy-time uncertainty relation
LMI-II Part 5 Lasers - A brief description

Class Notes [Physics of Molecules]
MPI Part 1 - Why things bind - Typical scales - Energetics of Ionic bonds
MPI Part 2 - The Complexity of the Quantum Mechanical Problem of a Molecule - An appreciation
MPI Part 3 - The Beauty of the Born-Oppenheimer Approximation and Big Picture of Molecular States
MPI Part 4 - Solving electronic part to obtain Molecular Orbitals (MO) by Linear Combination of Atomic Orbitals - LCAO - MO
MPI Appendix A (Revised) - Quantum Nature of Bonding - LCAO-MO in H2+ as example
MPI Part 5 - Filling MOs via Pauli Exclusion Principle - Bond Order - single, double, triple bonds, sigma and pi bonds
MPII Extension on Bonding - Hybridization - BeH2 - C2H4 - Graphene - CH4 - Diamond - Silicon and Delocalized electrons in Benzene
MPII Appendix (Optional) - Conceptual discussion on how sp hybridization emerges naturally from LCAO calculation - BeH2 case
MPIII Vibrational and Rotational Energies - Rotational Spectrum - Vibrational and Rotational Spectrum - Extract Bond Information from Spectrum - Greenhouse Gases

Class Notes [Miscellaneous Topics]
Tunneling Part 0 - Why Tunneling - Phenomena related to alpha particle decay
Tunneling Part 1 - Traveling Waves in QM - Difficulties in normalization - Ways out
Tunneling Part 2 Revised - Continuity Equation in QM and Probability Current Density
Tunneling Part 3 - Formalism-Transmission and Reflection Coefficients-Key Features in results
Physics of Nuclei - A crash module (understanding properties of nuclei using QM knowledge discussed)
Tunneling Part 4 - Alpha-decay as an Application of Tunneling
Tunneling Part 5 - More Applications (Fusion in Sun and ITER on Earth, STM, Field Emission, Resonant Tunneling, Quantum Cascade Laser)

Class Notes [Back Matter]
What have we done in Applied Quantum Mechanics?
Further Reading on all topics
List of constants and useful numbers

Sample Questions for Exercise Classes
Sample Questions SQ1,2,3 for Week 1 Exercise Classes
Sample Questions SQ4.5 for Week 2 Exercise Classes
Sample Questions SQ6,7 for Week 3 Exercise Classes
Sample Questions SQ8,9,10 for Week 4 Exercise Classes
Sample Questions SQ11,12,13 for Week 5 Exercise Classes
Sample Questions SQ14,15 for Week 6 Exercise Classes
Sample Questions SQ16,17 for Week 7 Exercise Classes
Sample Questions SQ18,19 for Week 8 Exercise Classes
Sample Questions SQ20,21 for Week 9 Exercise Classes
Sample Questions SQ22,23 for Week 10 Exercise Classes
Sample Questions SQ24,25,26 for Week 11 Exercise Classes
Sample Questions SQ27,28 for Week 12 Exercise Classes
Sample Questions SQ29,30,31 for Week 13 Exercise Classes

PHYS3021 2018-2019 Quantum Mechanics I notes

Problem Sets
Problem Set 1 (due 23 Jan 2019)
Problem Set 2 (due 30 Jan 2019)
Problem Set 3 (due 20 Feb 2019)
Problem Set 4 (due 1 March 2019)
Problem Set 5 - With revision marked (due 22 March 2019)
Problem Set 5 revised soft copy (due 22 March 2019)
Problem Set 6 (due 2 April 2019)
Problem Set 7 (with Revised Problem 7.3) (due 18 April 2019)

Erratum (Corrected typos on pages of class notes)