PHYS3022 Applied Quantum Mechanics (2019-2020 Term 2)
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PHYS3022 Applied Quantum Mechanics (2019-2020 Term 2)
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Class Notes [Front Matter]
  • PHYS3022 Time table and TA consultation hours & contacts -Term 2 2020
  • PHYS 3022 Applied Quantum Mechanics (Term 2 2019-2020) - Course Information - Assessment Mode - Academic honesty policy
  • PHYS 3022 Applied Quantum Mechanics - Course Learning Outcomes
  • List of books and Links to Reserved Books in Library - 2019-2020
  • Ch 0 - Overview and Style of the Course


    • Class Notes [Essential QM in previous course (Self-review/Self-study)]


    Class Notes [Quantum Theory of Hydrogen Atom - Key concepts (Almost correct version)]
  • PHYS 3021 Ch VIII (for revision) TISE problems of Spherically Symmetric Potential Energy Functions
  • PHYS 3021 Ch VIII Appendix A (Optional & for Revision) - The angular equation has Legendre Polynomials and Associated Legendre Polynomials as solutions
  • H-Atom Preparatory Part 1 - Spherical Harmonics and s-p-d orbitals (see PHYS 3021 Ch VIII for technical details)
  • H-Atom Preparatory Part 2 - Orbital Angular Momentum and Spherical Harmonics - and - 3D Rigid Rotor
  • Quantum Theory of Hydrogen Atom Part 1 - Key Features of Energy Eigenvalues and Labelling of Eigenfunctions
  • Quantum Theory of Hydrogen Atom Part 2 Visualization of Atomic Orbitals - Radial Probability Density - Bohr Model
  • Figures used in Quantum Theory of H-atom Part 2
  • Quantum Theory of Hydrogen Atom Part 3 - How well does the simplest model work in comparison with data
  • Quantum Theory of Hydrogen Atom (Optional) - Solving H-atom Radial Equation by Series Solution Method


    • Class Notes [Hermitian Operators - Definition, Properties, Generalized Uncertainty Relation]
  • Hermitian Operators Part 1 - Definition-Real eigenvalues-Orthonormal eigenstates-real expectation values
  • Hermitian Operators Part 2 - About two Hermitian Operators - Compatible quantities - Ehrenfest Theorem - General Uncertainty Relation


    • Class Notes [Methods (mostly techniques of approximations) in QM]
  • Cross Referencing: Summarizing Formal QM - Postulates of Quantum Mechanics
  • [LINK] to 12-minute discussion on Postulates of Quantum Mechanics [see also class notes]
  • AM Part 0 - Motivation - Why do we need approximation methods?
  • [LINK] to 15-minute clip on "Why do we need approximation methods?"
  • AM Part 1 (Typos corrected) - An Exact Formulation - Turning TISE into a Big Matrix Problem
  • [LINK] to 23-minute clip on Turning TISE into a Big Matrix Problem
  • AM Part 2 - The Variational Method (a simple but powerful method)
  • [LINK] to 25-minute clip on the Variational Method
  • AM Part 3 - First order perturbation theory - Hand-waving argument without math
  • [LINK] to 27-minute clip on Perturbation Theory - Hand waving argument without math
  • AM Part 4 - Time-independent Perturbation Theory - 1st and 2nd order (Formal Derivation and Physical Picture)
  • [LINK] to 38-minute clip on deriving 1st and 2nd order time-independent perturbation theory and meaning of the results
  • AM Part 5 - 1st and 2nd order pertubation theory makes simple by matrix viewpoint
  • [LINK] to 12-minute clip on Perturbation Results in Matrix Viewpoint
  • AM Part 6 - Time-independent DEGENERATE perturbation theory
  • [LINK] to 4-minute clip on Time-independent DEGENERATE perturbation theory
  • Summary on Tools in Approximation Toolbox


    • Class Notes [Angular Momentum in QM and Spin Angular Momentum]
  • Cross Reference - Orbital Angular Momentum and Spherical Harmonics - and - 3D Rigid Rotor (H-Atom Preparatory Part 2)
  • Angular Momentum in QM - General Results based on Commutation Relations
  • Spin Angular Momentum Part 1 - AM and Magnetic Dipole Moment - Effect of inhomogeneous B field
  • Spin Angular Momentum Part 2 - Stern Gerlach Expt - Key results on electron spin AM
  • Spin Angular Momentum Part 3 - Matrix Representation of Spin AM - Using Spin AM to learn QM
  • Spin Angular Momentum Part 3 (typos corrected) - Matrix Representation of Spin AM - Using Spin AM to learn QM
  • Spin Angular Momentum Part 4 - Math Structure and Postulates of QM from Spin AM
  • Summarizing Formal QM - Postulates of Quantum Mechanics


    • Class Notes [Physics of Atoms - More on Hydrogen, Beyond Hydrogen and the Periodic Table]
  • AP I Part 1 - Review on H-atom results and unexplained features (for revision or self-learning)
  • AP I Part 2 - Zeeman Effect ignoring effects of spin (Normal Zeeman Effect)
  • [LINK] to 21-minute clip on the Normal Zeeman Effect (ignoring spin effects)
  • AP I Part 3 - Spin Magnetic Dipole Moment and Spin Angular Momentum of Electron (mostly review)
  • [LINK] to 7-minute clip on Spin magnetic dipole moment and Spin angular momentum
  • AP I Part 4 - Total Angular Momentum and Two schemes of labelling atomic states
  • [LINK] to 23-minute clip on Total Angular Momentum and Two schemes of labelling atomic states
  • AP I Part 5 - Spin-Orbit Interaction (the physics behind and H'so)
  • [LINK] to 26-minute clip on Spin-Orbit Interaction (the physics behind and H'so)
  • AP I Part 6 - Spin-orbit interaction is partially responsible for the fine structure in atoms
  • [LINK] to 21-minute clip on Spin-orbit interaction is partially responsible for the fine structure in atoms
  • AP I Part 7 - Term Symbols for understanding data
  • AP I Part 8 - Basic QM explains large part of spectroscopic data but Lamb Shift needs QED
  • AP I Part 9 - Zeeman Effect revisited - Strong field case and Weak field case
  • AP I Part 10 - Hyperfine Structure and 21-cm Astronomy (with links to FAST and articles)
  • Optional Extension [with LINKS to references] - Frontier Topics links to precise H-atom spectroscopy [Anti-hydrogen spectroscopy, Proton size problem, Proton spin crisis]
  • AP II Part 1 - Hamiltonian of multi-electron atoms and Atoms are Many-electron problems hard to solve
  • AP II Part 2 - Helium atom ground state - perturbation - variational method - hints on effective single-electron problem
  • AP II Appendix A - Atomic units are commonly used in atomic and molecular physics
  • AP II Part 3 - Independent Particle Approximation - Basic ideas
  • AP II Appendix B - Hartree self-consistent approach in determining single-electron states
  • AP II Part 4 - Exchange symmetry and Multi-electron wavefunctions must be anti-symmetric
  • AP II Part 5 - Slater Determinant form of multi-electron wavefunctions and Pauli Exclusion Principle as a by-product
  • AP II Part 6 - Helium ground state has symmetric spatial part and anti-symmetric singlet spin part
  • AP II Part 7 - Adding two spin AMs - Singlet state is anti-symmetric and Triplet states are symmetric
  • AP II Part 8 - Helium lowest excited states and the Quantum Origin of Magnetism
  • AP II Part 9 - The Periodic Table and common-sense trends among atoms
  • AP II Optional Asides - Spin-orbit effect in atoms and the Hund's rules for filling electrons
  • AP II Appendix C - Quantum Revolution in your generation


    • Class Notes [Atomic transitions, Light-Matter Interaction and Approximation (cont
  • LMI Part 1 - Absorption and Emission Phenomena and form of Perturbation Term in electric dipole mechanism
  • LMI Part 2 - Prob Amplitute of transition - Absorption and Stimulated Emission carry same expression - Selection Rules and Transition Rates
  • LMI Part 3 - Einstein A and B coefficients and Relating them to QM results
  • LMI Part 4 - Spontaneous Emission rate - Lifetime of an excited state
  • LMI Part 5 - Long Lifetime states and Stimulated Emission are at the heart of LASER - Plus final remarks and references
  • LMI Appendix A (Optional) - Time-dependent Perturbation Theory
  • LMI Appendix B (Optional) - Generalizing to non-monochromatic incident light


    • Class Notes [Physics of Molecules]
  • MPI Part 1 - Typical numbers - Sense of why things bind - Energetics of ionic bonds
  • MPI Part 2 [revised] - QM Problems of Molecules are impossible to solve analytically - Appreciating the complexity
  • MPI Part 3 - Born-Oppenheimer Approximation - Electronic and Nuclear Motion parts of molecular problems - Molecular levels (the big picture)
  • MPI Part 4 - Electronic Part - Linear Combination of Atomic Orbitals LCAO is an effective approximation of understanding bonding - Illustrated by H2+ ion
  • MPI Appendix A (Optional) - Quantum Nature of Bonding in H2+ ion (LCAO-MO)
  • MPI Part 5 - LCAO and simple matrix math are behind the physics of bonding (sigma and pi bonds)
  • MPI Part 6 - LCAO is behind hydridization (sp, sp2, sp3) and delocalization of pi-electrons
  • MPII Part 1 - Putting back the nuclei motion and Total energy of molecular states
  • MPII Part 2 - Rotational levels and Rotational Spectrum in microwaves or far IR range gives bond length
  • MPII Part 3 - Transitions between vibrational levels and why CO2 and H2O are greenhouse gases
  • MPII Part 4 - Vibrational-Rotational Spectrum gives bond length and bond strength plus summary and further reading


    • Class Notes [Miscellaneous Topics (Optional)]
  • Tunneling Part 1 - Motivation - Traveling waves in QM
  • Tunneling Part 2 - Probability Current Density in Quantum Mechanics
  • Tunneling Part 3 - Tunneling with a single barrier - Key results to take home
  • Tunneling Part 4 - Back to Alpha Decays
  • Tunneling Part 5 - Other applications - STM - Field emission - Fusion energy from the Sun - etc


    • Class Notes [Back Matter]


    Sample Questions for Exercise Classes
  • Sample Questions SQ1,2,3 for Week 1 Exercise Classes
  • Sample Questions SQ4,5,6 for Week 2 Exercise Classes
  • Sample Questions SQ7,8 for Week 3 Exercise Classes
  • Sample Questions SQ9,10 for Week 4 Exercise Classes (via Zoom to be conducted by PM Hui)
  • Sample Questions SQ11,12 for Week 5 Exercise Classes (via Zoom to be conducted by TAs)
  • Sample Questions SQ13,14 for Week 6 Exercise Classes (via Zoom to be conducted by TAs)
  • Sample Questions SQ15,16,17 for Week 7 Exercise Classes (via Zoom to be conducted by TAs)
  • Sample Questions SQ18,19,20 for Week 8 Exercise Classes (via Zoom to be conducted by TAs)
  • Sample Questions SQ21,22 for Week 9 Exercise Classes (via Zoom to be conducted by TAs)
  • Sample Questions SQ23,24 for Week 10 Exercise Classes (via Zoom to be conducted by TAs)
  • Sample Questions SQ25,26,27 for Week 11 Exercise Classes (via Zoom to be conducted by TAs)
  • Sample Questions SQ28,29 for Week 12 Exercise Classes (via Zoom to be conducted by TAs)
  • Sample Questions SQ30,31,32 for Week 13 Exercise Classes (conducted by TAs via Zoom)


    • Solutions to Sample Questions for Exercise Classes
  • Solutions to Sample Questions 1 - 3
  • Solutions to Sample Questions 4 - 6
  • Solutions to Sample Questions 7 - 8
  • SQ9 [LINK] to 12-minute clip on Postulates of Quantum Mechanics
  • Solutions to SQ10 with discussion on implications (massless fermion, graphene, Dirac equation)
  • Solutions to Sample Questions 11 - 12
  • Solutions to Sample Questions 13, 14
  • Solutions to Sample Questions 15,16,17
  • Solutions to Sample Questions 21, 22
  • Solutions to Sample Questions 18, 19, 20
  • Solutions to Sample Questions 28, 29
  • Solutions to Sample Questions 23, 24
  • Solutions to Sample Questions 25, 26, 27
  • Solutions to Sample Questions 30, 31, 32


    • Problem Sets
  • Problem Set 1 (due 21 Jan 2020)
  • Problem Set 2 (due 14 Feb 2020) [submit your work via email]
  • Problem Set 2 [2.1(e) revised] (due 14 Feb 2020) [submit your work via email]
  • Problem Set 3 (due 3 March 2020 before 23:00 via email)
  • Problem Set 4 (due 17 March 2020) [submit your work via email]
  • Problem Set 5 (due 20 April 2020) [submit your work via email]
  • Problem Set 6 (due 2 May 2020) [submit your work via email]


    • Solutions to Problem Sets


    Other Learning Materials and Announcements
  • Further Reading on all topics


    • Erratum (Corrected typos on pages of class notes)