Undergraduate Course: Foundations of Quantum Mechanics (PHYS09051)

Course Outline
School	School of Physics and Astronomy	College	College of Science and Engineering
Course type	Standard	Availability	Available to all students
Credit level (Normal year taken)	SCQF Level 9 (Year 3 Undergraduate)	Credits	10
Home subject area	Undergraduate (School of Physics and Astronomy)	Other subject area	None
Course website	None	Taught in Gaelic?	No
Course description	This course covers fundamentals of quantum mechanics and this applications to atomic and molecular systems. The course includes non-relativistic quantum mechanics, supplying the basic concepts and tools needed to understand the physics of atoms, molecules, and the solid state. One-dimensional wave mechanics is reviewed. The postulates and calculational rules of quantum mechanics are introduced, including Dirac notation. Angular momentum and spin are shown to be quantized, and the corresponding wave-function symmetries are discussed. The eigenvalue equation for the energy is solved for a number of important cases, including the harmonic oscillator and the Hydrogen atom. Approximate methods of solution are studied, including time-independent perturbation theory, with application to atomic structure.

Entry Requirements (not applicable to Visiting Students)
Pre-requisites		Co-requisites
Prohibited Combinations	Students MUST NOT also be taking Quantum Mechanics (PHYS09053)	Other requirements	None
Additional Costs	None

Information for Visiting Students
Pre-requisites	None
Displayed in Visiting Students Prospectus?	No

Course Delivery Information

Delivery period: 2013/14 Semester 1, Available to all students (SV1)			Learn enabled: No	Quota: None
Web Timetable	Web Timetable
Course Start Date	16/09/2013
Breakdown of Learning and Teaching activities (Further Info)	Total Hours: 100 ( Lecture Hours 22, Seminar/Tutorial Hours 22, Revision Session Hours 1, Programme Level Learning and Teaching Hours 2, Directed Learning and Independent Learning Hours 53 )
Additional Notes
Breakdown of Assessment Methods (Further Info)	Written Exam 80 %, Coursework 20 %, Practical Exam 0 %
Exam Information
Exam Diet	Paper Name	Hours:Minutes
Main Exam Diet S2 (April/May)	Foundations of Quantum Mechanics (PHYS09051)	2:00

Delivery period: 2013/14 Semester 1, Part-year visiting students only (VV1)			Learn enabled: No	Quota: None
Web Timetable	Web Timetable
Course Start Date	16/09/2013
Breakdown of Learning and Teaching activities (Further Info)	Total Hours: 100 ( Lecture Hours 22, Seminar/Tutorial Hours 22, Revision Session Hours 1, Programme Level Learning and Teaching Hours 2, Directed Learning and Independent Learning Hours 53 )
Additional Notes
Breakdown of Assessment Methods (Further Info)	Written Exam 80 %, Coursework 20 %, Practical Exam 0 %
Exam Information
Exam Diet	Paper Name	Hours:Minutes
Main Exam Diet S1 (December)		2:00

Summary of Intended Learning Outcomes
- State in precise terms the foundational principles of quantum mechanics and how they relate to broader physical principles. - Devise and implement a systematic strategy for solving a complex problem in quantum mechanics by breaking it down into its constituent parts. - Apply a wide range of mathematical techniques to build up the solution to a complex physical problem. - Use experience and intuition gained from solving physics problems to predict the likely range of reasonable solutions to an unseen problem. - Resolve conceptual and technical difficulties by locating and integrating relevant information from a diverse range of sources.

Assessment Information
Exam 80% and coursework 20%

Special Arrangements
None

Additional Information
Academic description	Not entered
Syllabus	- Wave mechanics in 1D; wavefunctions and probability; eigenvalues and eigenfunctions; the superposition principle. - Notions of completeness and orthogonality, illustrated by the infinite 1D well. - Harmonic oscillator. Parity. Hermitian operators and their properties. - Postulates of quantum mechanics; correspondence between wavefunctions and states; representation of observables by Hermitian operators; prediction of measurement outcomes; the collapse of the wavefunction. - Compatible observables; the generalised Uncertainty Principle; the Correspondence Principle; time evolution of states. - Heisenberg's Equation of Motion. Constants of motion in 3D wave mechanics: separability and degeneracy in 2D and 3D. - Angular momentum. Orbital angular momentum operators in Cartesian and polar coordinates. Commutation relations and compatibility. Simultaneous eigenfunctions and spherical harmonics. The angular momentum quantum number L and the magnetic quantum number mL. - Spectroscopic notation. Central potentials and the separation of Schrodinger's equation in spherical polars. - The hydrogen atom: outline of solution, energy eigenvalues, degeneracy. - Radial distribution functions, energy eigenfunctions and their properties. Dirac notation. - Applications of operator methods; the harmonic oscillator by raising and lowering operator methods. - Angular momentum revisited. Raising and lowering operators and the eigenvalue spectra of J2 and Jz. - Condon-Shortley phase convention. Matrix representations of the angular momentum operators; the Pauli spin matrices and their properties. - Properties of J=1/2 systems; the Stern-Gerlach experiment and successive measurements. Regeneration. - Spin and two-component wavefunctions. The Angular Momentum Addition Theorem stated but not proved. Construction of singlet and triplet spin states for a system of 2 spin-1/2 particles. - Identical particles. Interchange symmetry illustrated by the helium Hamiltonian. The Spin-Statistics Theorem. Two-electron wavefunctions. The helium atom in the central field approximation: ground-state and first excited-state energies and eigenfunctions. The Pauli Principle. Exchange operator. - Quantum computing, entanglement and decoherence. - Introduction to Hilbert spaces. - Basic introduction to linear operators and matrix representation. - Advanced concepts in addition of angular momenta: the uncoupled and coupled representations. Degeneracy and measurement. Commuting sets of operators. Good quantum numbers and maximal measurements.
Transferable skills	Not entered
Reading list	Not entered
Study Abroad	Not entered
Study Pattern	Not entered
Keywords	FQMech

Contacts
Course organiser	Prof Luigi Del Debbio Tel: (0131 6)50 5212 Email: luigi.del.debbio@ed.ac.uk	Course secretary	Miss Jillian Bainbridge Tel: (0131 6)50 7218 Email: J.Bainbridge@ed.ac.uk