Undergraduate Course: Quantum Mechanics (PHYS09053)
Course Outline
School  School of Physics and Astronomy 
College  College of Science and Engineering 
Credit level (Normal year taken)  SCQF Level 9 (Year 3 Undergraduate) 
Availability  Available to all students 
SCQF Credits  20 
ECTS Credits  10 
Summary  This twosemestered course covers fundamentals of quantum mechanics and its applications to atomic and molecular systems.
The first semester covers nonrelativistic quantum mechanics, supplying the basic concepts and tools needed to understand the physics of atoms, molecules, and the solid state. Onedimensional 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 wavefunction symmetries are discussed. The Schrodinger equation is solved for a number of important cases, including the harmonic oscillator and the Hydrogen atom. The fundamentals of time independent perturbation theory will be introduced as a means of approximating solutions to complex problems.
The second semester deals principally with atomic structure, the interaction between atoms and fields, and the atom atom interactions in molecular physics. The course presents a detailed treatment of the hydrogen atom, including spinorbit coupling, the fine structure, and the hyperfine interactions. Identical particles are reviewed in the context of electron electron interactions; applications include the Helium atom, Coulomb/exchange integrals, and alkali metals energy levels. Atomfield interactions are discussed, leading to dipole transitions, the Zeeman effect, the Lande gfactor, and the Stark effect. Finally atomatom interactions are presented, leading to the study of molecular binding, molecular degrees of freedom (electronic, vibrational, and rotational), elementary group theory considerations and molecular spectroscopy. 
Course description 
Quantum Mechanics (semester 1):
 Review and advanced application of wave mechanics to important potentials (Dirac well, harmonic potential, radial symmetric potentials)
 Applications to solving the required ordinary and partial differential equations (series expansion, applications of special functions, and separation of variables)
 Postulates of quantum mechanics and mathematical foundations
 Operator algebra including commutation relations and relation to matrix algebra and links to linear algebra techniques already developed previously
 Dirac notation and application linking to linear algebra
 Ladder operators introduced through revisiting the harmonic oscillator
 General angular momentum including operator algebra and application to spin as a special case; addition of angular momentum will be introduced
 Introduction to time independent perturbation theory as an application of the techniques introduced in semester 1
Quantum & Atomic Physics (semester 2):
 Timeindependent perturbation theory for nondegenerate systems: the firstorder formalism for energy eigenvalues and eigenstates. Higher order corrections outlined.
 Applications of perturbation theory: the ground state of helium, spinorbit effects in hydrogenlike atoms.
 Nondegenerate timeindependent perturbation theory: the firstorder formulae for energy shifts and wavefunction mixing. Higherorders.
 Timeindependent perturbation theory for degenerate systems: the firstorder calculation of energy shifts. Lifting of degeneracy by perturbations. Special cases.
 Hydrogen fine structure. Kinetic energy correction, spinorbit correction and Darwin correction. RussellSaunders notation, Zeeman effect, Stark effect, other atomic effects.
 Outline of multielectron atoms and their treatment in the central field approximation. Slater determinants.
 The RayleighRitz variational method. Ground state of Hydrogen as an example. Result for Helium atom. Variational bounds for excited states.
 Self consistent field theory (Hartree), density functional theory. Manyparticle wavefunction, exchange symmetry and correlations.
 The H2+ ion & molecular bonding. BornOppenheimer approximation. Variational estimates of the groundstate energy. Brief discussion of rotational and vibrational modes. Van der Waals force.
 Periodic potentials, reciprocal lattice, softening of band edge.
 Quantization of lattice vibrations (phonons). Linear chains.
 Timedependent problems: timedependent Hamiltonians, firstorder perturbation theory, transition probabilities.
 Transitions induced by a constant perturbation: Fermi's Golden Rule. Harmonic perturbations and transitions to a group of states.
 Interaction of radiation with quantum systems. Electromagnetic radiation. Interaction with a 1electron atom. The dipole approximation. Absorption and stimulated emission of radiation.
 Spontaneous emission of radiation. Einstein A and B coefficients. Electric dipole selection rules. Parity selection rules.
 Semiclassical approximation  WKB approximation.
 Quantum scattering theory. Differential and total crosssections. The Born approximation via Fermi's Golden Rule. Density of states, incident flux, scattered flux. Differential crosssection for elastic scattering. Partial waves.

Information for Visiting Students
Prerequisites  None 
High Demand Course? 
Yes 
Course Delivery Information

Academic year 2015/16, Available to all students (SV1)

Quota: None 
Course Start 
Full Year 
Timetable 
Timetable 
Learning and Teaching activities (Further Info) 
Total Hours:
200
(
Lecture Hours 44,
Seminar/Tutorial Hours 44,
Formative Assessment Hours 3,
Revision Session Hours 1,
Programme Level Learning and Teaching Hours 4,
Directed Learning and Independent Learning Hours
104 )

Assessment (Further Info) 
Written Exam
80 %,
Coursework
20 %,
Practical Exam
0 %

Additional Information (Assessment) 
Coursework 20%
Examination 80% 
Feedback 
Not entered 
Exam Information 
Exam Diet 
Paper Name 
Hours & Minutes 

Main Exam Diet S2 (April/May)  Quantum Mechanics (PHYS09053)  3:00  
Learning Outcomes
On completion of this course, the student will be able to:
 State the postulates and foundations of quantum mechanics
 Solve differential equations in related to quantum mechanical problems using techniques applied in this course (particularly series expansion, separation variables, and special functions)
 Understand and apply Dirac notation and operator algebra to problems in quantum mechanics and linear algebra
 Understand ladder operators and their properties
 Be able to apply generalised angular momentum techniques to problems and also have an understanding of the commutation relations and how to derive these

Reading List
Albert Messiah, "Quantum Mechanics"
Claude Cohen Tannoudji, "Quantum Mechanics  vol 1"
L. D. Landau ad E. M. Lifshitz, "Quantum Mechanics: NonRelativistic Theory" 
Additional Information
Graduate Attributes and Skills 
Not entered 
Special Arrangements 
None 
Keywords  QMech 
Contacts
Course organiser  Dr Christopher Stock
Tel: (0131 6)50 7066
Email: C.Stock@ed.ac.uk 
Course secretary  Mrs Siobhan Macinnes
Tel: (0131 6)51 3448
Email: Siobhan.MacInnes@ed.ac.uk 

