MATHEMATICAL PHYSICS FOR B.Sc. PROGRAMMES
FIRST YEAR COURSES
COMMON COURSE
The First Year common programme
in Mathematical Physics consists of the modules MP110 and MP112. There are three formal lectures per week throughout
the year. In addition there is one tutorial per
week throughout both semesters. There are two three
hour examination papers in the examination period. Continuous
assessment of the modules may count for up to 15% of the first year mark
applied to the student’s advantage.
MP110 MECHANICS I
& SPECIAL RELATIVITY
36 lecture hours
7.5 ECTS credits
Linear kinematics and
dynamics of a particle and of a system of particles. Principles
of momentum and energy. Particle dynamics in more
than one dimension. Vector methods. Motion in a circle,
simple harmonic motion, motion under constant gravity.
Introduction to special relativity: Postulates
of special relativity, spacetime, time dilation, length contraction,
Doppler shift.
MP112 MECHANICS 2
& MODERN PHYSICS
36 lecture hours
7.5 ECTS credits
Centre of mass and moment of inertia. Two dimensional dynamics of a system of particles, including
collision and impulse. Motion of a rigid body. Two dimensional statics - friction problems, frameworks
and virtual work. Motion under a central force. Vector analysis and some potential theory.
Quantum Physics: Photoelectric effect, blackbody
radiation, wave-particle duality, Heisenberg uncertainty principle.
Bachelor
of Science (Theoretical Physics and Computer Science).
MH205
First Year Courses
Mathematical Physics, Computer Science, Mathematics
and Experimental Physics.
MATHEMATICAL PHYSICS
FOR HONOURS THEORETICAL PHYSICS AND MATHEMATICS DEGREE
MH206
First Year Courses
Double Mathematical Physics and Double Mathematics.
DOUBLE MATHEMATICAL PHYSICS COURSE
The First Year Double Mathematical
Physics programme for the Theoretical Physics and Mathematics course is
listed below.
There are six formal lectures
and two tutorials per week. There are three 3 hour examination papers in
the Examination period. Students take the modules MP110, MP112, MP120, MP201
and MP202. Continuous assessment of the modules may count for up to 15%
of the first year mark applied to the student’s
advantage.
MP120 MATHEMATICAL
PHYSICS
24 lecture hours
5 ECTS credits
Differential Equations: First
order equations and integrating factors, second order, linear equations with
constant coefficients.
Mechanics: Newton's second law as differential
equation, variable mass problems.
Thermodynamics: Kinetic theory of gases, Maxwell-Boltzmann
distribution, temperature, ideal gases, entropy and free energy, first
and second laws of thermodynamics.
COMMON COURSE
The modules for the Second Year
Mathematical Physics course are listed below. There are four lectures and
two tutorials per week. There are two 3 hour examination papers in the
Examination period. Continuous assessment of the modules may count for up
to 15% of the second year mark applied to the student’s advantage.
MP201 MATHEMATICAL
METHODS
24 lecture hours
5 ECTS credits
Introduction to partial
derivatives. Integrals: surface, volume, line. Gauss's and Stokes's theorems. Orthogonal
expansions. Fourier Series. Calculus
of variations.
MP202 MECHANICS
24 lecture hours
5 ECTS credits
Motion of a particle
in one dimension. Motion in a resisting medium. Damped harmonic oscillator. Forced
damped harmonic oscillator. Equations of motion
of a particle in two or three dimensions. Projectiles
under resistance. The Kepler problem. Motion of a system of particles. Rigid
body motion in two dimensions. Lagrange's equations. Hamilton's equations. Wave theory.
MP231 ELECTRICITY
AND MAGNETISM I
24 lecture hours
5 ECTS credits
Electrostatic field,
charge, potential and flux. Gauss's and Stokes's
theorems. Capacitance. Dielectrics and polarisation. Energy of an electric field. magnetic
effects of currents.
MP232 ELECTRICITY
& MAGNETISM 2 AND STATISTICAL THERMODYNAMICS
24 lecture hours
5 ECTS credits
Magnetostatic field. Magnetic vector potential. The
Biot-Savart law. Mutual and self
induction. Magnetic materials. Ampere's law. Magnetic energy. Uniqueness of solution of
potential problems and
the method of images. Neumann and Lenz's laws of induction.
Maxwell equations.
The Boltzmann distribution
and macroscopic thermodynamics. The equipartition
theorem and the ideal gas equation. Quantum statistical
mechanics. Applications to specific heats. Ideal particles. Fermi-Dirac and
Bose-Einstein distributions. Planck's radiation
law.
Bachelor
of Science (Theoretical Physics and Computer Science).
MH205
Second Year Courses
Mathematical Physics, Computer Science and Mathematics.
MATHEMATICAL PHYSICS FOR HONOURS THEORETICAL PHYSICS
AND MATHEMATICS DEGREE
MH206
Second Year Courses
The modules offered are the same as in the third
year of the Honours Mathematical
GENERAL COURSE
The Third Year General programme in Mathematical
Physics consists of the following set of modules: MP350, MP352, MP353 and
MP354.
There are four lectures and two tutorials per week. In addition there
is a two hour laboratory per week for one semester in connection with MP354. There
are two three hour examination papers in the Examination period. Continuous
assessment of MP354 counts for up to 15% of the overall
third year mark in Mathematical Physics.
There are six lectures and two
tutorials per week. In addition there is two hours laboratory work for
one semester which is associated with MP354. There are three 3 hour examination
papers in the Examination period. Continuous assessment of MP354 counts for up to 15% of the overall
third year honours mark in Mathematical Physics. 50% of the third year
result will be carried over to the final year Double Honours Degree in
Mathematical Physics applicable to the students’ advantage. 35% of the third year result will be carried over to
the final year Single Honours Degree in Theoretical Physics applicable
to the students advantage.
MP350 CLASSICAL MECHANICS
24 lecture hours
5 ECTS credits
Lagrange theory. Variational principles. Hamilton's Principle.
Lagrange equations.
Lagrange multipliers. Central forces. Two-body motion: bound states.
Rigid Body Motion. Euler's
theorem. Euler's equation of motion. The heavy symmetrical
top.
Small oscillations Hamiltonian theory. The
canonical equations.
Canonical transformations.
Generating functions. Poisson brackets.
Hamilton-Jacobi theory:
The Hamilton-Jacobi equation. Action-angle variables.
MP352 SPECIAL RELATIVITY
24 lecture hours
5 ECTS credits
Inertial frames. Michelson-Morley and Fizeau experiments. Stellar aberration. Principle of
special relativity and
Lorentz transformations. Length contraction and time
dilatation.
Relativistic mechanics.
Particle collisions, centre of mass systems and
threshold energies.
Covariance of electromagnetic
field equations and their covariant formalism. Tensors.
MP353 FLUID MECHANICS
24 lecture hours
5 ECTS credits
Kinematics of fluid
motion. Euler's equations, steady flow. Bernoulli's equation. Circulation.
Kelvin's theorem. Velocity potential for two and three dimensional flows. Sources, sinks
and doublets. The complex potential. Method of
images. Vortex lines. Supersonic
flow.
Viscosity. Viscous flow. Navier Stokes' equation. Reynold's number. Turbulence.
Poiseuille flow. Couette flow. Kolmogorov Scaling.
12 lecture hours
+ 24 laboratory hours
5 ECTS credits
Each Lecture is followed
by 2 hours laboratory work
Introduction to Unix. Introduction to C. Error, accuracy
and stability.
Integration. Root finding. Newton-Raphson. Ordinary Differential Equations:
Euler method. Runge-Kutta method.
MP361 MATHEMATICAL
METHODS I
24 lecture hours
5 ECTS credits
Calculus in several
variables. Linear differential equations with constant
and variable coefficients.
Construction of Green's
functions. Solution by power series, including treatment
of singular points.
Legendre, Laguerre,
Hermite and Bessel polynomials. Fourier Series. Boundary
value problems in
one variable.
MP362 MATHEMATICAL
METHODS 2
24 lecture hours
5 ECTS credits
Sturm-Liouville theory
and expansion in orthogonal bases. Fourier and Laplace transforms. Partial Differential equations: Heat
equation, Wave equation, Laplace's equation. Spherical harmonics. Green's
functions for boundary value problems.Complex analysis up to Cauchy's residue
theorem.
Bachelor
of Science (Theoretical Physics and Computer Science).
MH205
Third Year Courses
Double Honours Mathematical Physics and Double
Honours Computer Science.
MATHEMATICAL PHYSICS FOR HONOURS THEORETICAL PHYSICS
AND MATHEMATICS DEGREE
MH206
Third Year Courses
The modules offered are the same as in the 4th year of the Double Honours Mathematical Physics
Degree (see below)
FOURTH YEAR COURSES
The modules for the final year Single Honours
course in Theoretical Physics and the Double Honours course in Mathematical
Physics are listed below.
For the Single Honours course in Theoretical
Physics students take all the listed modules. There
are 12 lectures and four tutorials per week. In
addition for one semester there are two hours laboratory work per week and
project work associated with module MP468. There are 5 three hour written examination papers at
the end of the second semester. Continuous assessment
and project work associated with MP468 will count for up to 15% of the
fourth year mark in Theoretical Physics. The final
degree result will be based on 65% of the fourth year result plus 35%
of the third year result. The latter is applied
to the student's advantage.
Double Honours students in Mathematical
Physics take modules (a) MP462 and MP463 plus optional modules from the
following groups of modules which add up to 20 ECTS. (b)
MP460 and MP461 (10 ECTS), (c) MP464 and MP465 (10 ECTS), (d) MP466 and
MP467 (10 ECTS) and (e) MP468 and MP470 (20 ECTS). The final degree result in Mathematical Physics will
be based on 50% of the fourth year mark plus 50% of the third year mark. The latter is applied to the students advantage.
MP460 THERMODYNAMICS
24 lecture hours
5 ECTS credits
0th law of thermodynamics (definition
of temperature).
Ideal gas law, kinetic theory of
gases, Van der Waal's equation.
Maxwell-Boltzmann distribution.
1st law of thermodynamics.
2nd law of thermodynamics, (Carnot
cycles, entropy, Boltzmann's H-theorem).
3rd law of thermodynamics.
Thermodynamic functions (Helmholz
and Gibb's functions).
Legendre transforms (Gibb's surfaces,
Gibb's rule of phases, Gibbs-Duhem relation).
Maxwell's equations.
MP461 STATISTICAL
MECHANICS
24 lecture hours
5 ECTS credits
Partition functions (simple sub-systems,
ideal gas, simple solids, ferro-magnet, Ising
model). Micro-canonical and grand
canonical ensembles. Phase transitions and critical phenomena. Bose-Einstein
and Fermi-Dirac statistics. Bose-Einstein condensation (super-conductors and
super-fluids). Information theoretic approach to entropy and partition function.
MP462 QUANTUM MECHANICS
I
24 lecture hours
5 ECTS credits
Stern-Gerlach Experiments
Rotation of Basis States and Matrix
Mechanics
Angular Momentum
Time Evolution
A System of Two Spin-2 Particles.
Bell Inequalities.
MP463 QUANTUM MECHANICS
2
24 lecture hours
5 ECTS credits
Wave Mechanics in One Dimension
The One-Dimensional Harmonic Oscillator
Translational and Rotational Symmetry
in the Two-Body Problem
Bound States of Central Potentials
Perturbation Theory
MP464 SOLID STATE
PHYSICS
24 lecture hours
5 ECTS credits
Crystal Structure
Free Electron Theory of Metals
Energy Bands
Semiconductors
Diamagnetism and Paramagnetism
MP465 ELECTROMAGNETISM
24 lecture hours
5 ECTS credits
Review of Maxwell Equations in
vacuo
Scalar and vector potentials
Multipole expansions in electrostatics
Multipole expansions in magnetostatics
Dielectrics
Diamagnetism
and Paramagnetism
Maxwell's Equations in ponderable
media
Waveguides
Radiation from simple systems:
multipole expansions and energy transport
Co-variant formalism of electromagnetism,
gauge invariance
MP466 PARTICLE PHYSICS
24 lecture hours
5 ECTS credits
Introduction to Forces and Particles
The four forces; classification
of leptons, hadrons, mesons,
baryons; strangeness, gravitons
The Quark model:
Quark model of mesons and baryons;
charm (J/Psi); QCD;
asymptotic freedom
Electro-weak theory
Isospin; neutrinos; Higg's bosons;
electro-weak interactions;
neutrino masses
Symmetries
Conservation laws; discrete symmetries
(CPT); C, P and T violation
(K_L-K_S oscillations)
Grand Unification:
Grand unification; proton decay;
super-symmetry
Current developments:
Elementary discussion of string
theory, current topics
MP467 COSMOLOGY
24 lecture hours
5 ECTS credits
Star Formation:
Jean's mass; PP-chain and CNO-cycle.
Stellar Structure:
Hydro-static equilibrium; radiation
transport; Eddington limit
Degenerate Stars:
Super-novae; white dwarves; neutron
stars; pulsars; black-holes
Binary systems:
Gravitational radiation
Galactic structure and evolution:
Active galactic nuclei; radio
galaxies; quasars
Cosmology:
Big Bang; micro-wave background
radiation; cosmological constant;
nucleo-synthesis; inflation
Astro-particle physics:
Cosmic rays; monopoles; dark
matter
MP468 COMPUTATIONAL
PHYSICS II
12 lecture hours
+ 24 hours laboratory + 20 hours project work
12 ECTS credits
Partial Differential
Equations. Elliptic equations - Laplace's equation. Hyperbolic
equations
Wave equations. Parabolic equations - Diffusion. Conservative
methods - continuity
equation. Matrix eigenvalue problems - Schroedinger equation. Monte Carlo Methods and
Simulation - random
number generators, integration, Metropolis algorithm.
MP470 CHAOS, NONLINEAR
DYNAMICS & QUANTUM INFORMATION PROCESSING
36 lecture hours
8 ECTS credits
Fixed points, limit cycles and strange
attractors.
Iterated maps.
Quadratic maps: Period doubling,
Quasi periodicity, devil's staircase, Farey tree.
Universality. Intermittency route
to chaos.
Hamiltonian systems.
Lyapunov exponents, Kolmogorov-
Sinai entropy.Concept of Dimension. Fractals
and multifractals.
Fundamental Concepts of Quantum
Information processing.
Introduction to Quantum Mechanics
Introduction to computer science
Quantum Circuits
Quantum Fourier Transform and
its applications
Quantum search algorithm
Physical realisations of quantum
information processors
Bachelor of Science (Theoretical Physics and
Computer Science).
MH205
Fourth Year Courses
Double Honours Mathematical Physics and Double
Honours Computer Science.
MATHEMATICAL PHYSICS FOR B.A. PROGRAMMES
COMMON/GENERAL COURSE
The First Year common programme
in Mathematical Physics consists of the modules MP110 and MP112. There are three formal lectures per week throughout
the year. In addition there is one tutorial per
week throughout both semesters. There are two three
hour examination papers in the examination period. Continuous
assessment of the modules may count for up to 15% of the first year mark
applied to the student’s advantage.
MP110 MECHANICS I
& SPECIAL RELATIVITY
36 lecture hours
7.5 ECTS credits
Linear kinematics and
dynamics of a particle and of a system of particles.
Principles of momentum and energy. Particle
dynamics in more than one dimension. Vector methods. Motion
in a circle, simple harmonic motion, motion under constant gravity.
Introduction to special relativity: Postulates
of special relativity, spacetime, time dilation, length contraction,
Doppler shift.
MP112 MECHANICS 2
& MODERN PHYSICS
36 lecture hours
7.5 ECTS credits
Centre of mass and moment of inertia. Two dimensional dynamics of a system of particles, including
collision and impulse. Motion of a rigid body. Two dimensional statics - friction problems, frameworks
and virtual work. Motion under a central force. Vector analysis and some potential theory.
Quantum Physics: Photoelectric effect, blackbody
radiation, wave-particle duality, Heisenberg uncertainty principle.
The first year Honours Mathematical Physics
programme consists of four lectures and two tutorials per week. Students take MP110, MP112, MP120.
DOUBLE MATHEMATICAL
PHYSICS FOR THE BA HONOURS
MATHEMATICAL SCIENCE COURSE
The First Year Double Mathematical
Physics programme for the Mathematical Science course is listed below.
There are six formal lectures
and two tutorials per week. There are three 3 hour examination papers in
the Examination period. Students take the modules MP110, MP112, MP120, MP201
and MP202. Continuous assessment of the modules may count for up to 15%
of the first year mark applied to the student’s
advantage.
MP120 MATHEMATICAL
PHYSICS
24 lecture hours
5 ECTS credits
Differential Equations: First
order equations and integrating factors, second order, linear equations
with constant coefficients.
Mechanics: Newton's second law as differential
equation, variable mass problems.
Thermodynamics: Kinetic theory of gases, Maxwell-Boltzmann
distribution, temperature, ideal gases, entropy and free energy, first
and second laws of thermodynamics.
COMMON/GENERAL COURSE
The modules for the Second Year
Mathematical Physics course are listed below. There are four lectures and
two tutorials per week. There are two 3 hour examination papers in the
Examination period. Continuous assessment of the modules may count for up
to 15% of the second year mark applied to the student’s advantage.
MP201 MATHEMATICAL
METHODS
24 lecture hours
5 ECTS credits
Introduction to partial
derivatives. Integrals: surface, volume, line. Gauss's and Stokes's theorems. Orthogonal
expansions. Fourier Series. Calculus
of variations.
MP202 MECHANICS
24 lecture hours
5 ECTS credits
Motion of a particle
in one dimension. Motion in a resisting medium. Damped harmonic oscillator. Forced
damped harmonic oscillator. Equations of motion
of a particle in two or three dimensions. Projectiles
under resistance. The Kepler problem. Motion of a system of particles. Rigid
body motion in two dimensions. Lagrange's equations. Hamilton's equations. Wave theory.
MP231 ELECTRICITY
AND MAGNETISM I
24 lecture hours
5 ECTS credits
Electrostatic field,
charge, potential and flux. Gauss's and Stokes's
theorems. Capacitance. Dielectrics and polarisation. Energy of an electric field. magnetic
effects of currents.
MP232 ELECTRICITY
& MAGNETISM 2 AND STATISTICAL THERMODYNAMICS
24 lecture hours
5 ECTS credits
Magnetostatic field. Magnetic vector potential. The Biot-Savart
law. Mutual and self
induction. Magnetic materials. Ampere's law. Magnetic energy. Uniqueness of solution of
potential problems
and the method of images. Neumann and Lenz's laws
of induction.
Maxwell equations.
The Boltzmann distribution
and macroscopic thermodynamics. The equipartition
theorem and the ideal gas equation. Quantum statistical
mechanics. Applications to specific heats. Ideal particles. Fermi-Dirac and
Bose-Einstein distributions. Planck's radiation
law.
THIRD YEAR BA GENERAL MATHEMATICAL PHYSICS
COURSE
The Third Year General programme in Mathematical
Physics consists of the following set of modules: MP350, MP352, MP353
and MP354. There are four lectures and two
tutorials per week. In addition there is a two hour laboratory per week
for one semester in connection with MP354. There
are two three hour examination papers in the Examination period. Continuous
assessment of MP354 counts for up to 15% of the overall
third year mark in Mathematical Physics.
SECOND YEAR BA MATHEMATICAL
PHYSICS COURSE
SECOND YEAR BA MATHEMATICAL SCIENCE COURSE
There are six lectures and two tutorials per
week. In addition there is two hours laboratory work for one semester
which is associated with MP354. There are three 3 hour examination
papers in the Examination period. Continuous assessment of MP354 counts for up to 15% of the overall
third year honours mark in Mathematical Physics. 50% of the third year
result will be carried over to the final year Double Honours Degree in Mathematical
Physics applicable to the students’ advantage. 35%
of the third year result will be carried over to the final year Single
Honours Degree in Theoretical Physics applicable to the students advantage.
MP350 CLASSICAL MECHANICS
24 lecture hours
5 ECTS credits
Lagrange theory. Variational principles. Hamilton's Principle.
Lagrange equations.
Lagrange multipliers. Central forces. Two-body
motion: bound states.
Rigid Body Motion.
Euler's theorem. Euler's equation of motion. The heavy symmetrical
top.
Small oscillations Hamiltonian theory.
The canonical equations.
Canonical transformations.
Generating functions. Poisson brackets.
Hamilton-Jacobi theory:
The Hamilton-Jacobi equation. Action-angle variables.
MP352 SPECIAL RELATIVITY
24 lecture hours
5 ECTS credits
Inertial frames. Michelson-Morley and Fizeau experiments. Stellar aberration. Principle of
special relativity
and Lorentz transformations. Length contraction and
time dilatation.
Relativistic mechanics. Particle collisions, centre of mass systems and threshold
energies.
Covariance of electromagnetic
field equations and their covariant formalism. Tensors.
MP353 FLUID MECHANICS
24 lecture hours
5 ECTS credits
Kinematics of fluid
motion. Euler's equations, steady flow. Bernoulli's equation. Circulation.
Kelvin's theorem. Velocity potential for two and three dimensional flows. Sources, sinks
and doublets. The complex potential. Method of
images. Vortex lines. Supersonic
flow.
Viscosity. Viscous flow. Navier Stokes' equation. Reynold's number. Turbulence.
Poiseuille flow. Couette flow. Kolmogorov Scaling.
12 lecture hours
+ 24 laboratory hours
5 ECTS credits
Each Lecture is followed
by 2 hours laboratory work
Introduction to Unix. Introduction to C. Error, accuracy
and stability.
Integration. Root finding. Newton-Raphson. Ordinary Differential Equations:
Euler method. Runge-Kutta method.
MP361 MATHEMATICAL
METHODS I
24 lecture hours
5 ECTS credits
Calculus in several
variables. Linear differential equations with
constant and variable coefficients.
Construction of Green's
functions. Solution by power series, including
treatment of singular points.
Legendre, Laguerre,
Hermite and Bessel polynomials. Fourier Series. Boundary
value problems in
one variable.
MP362 MATHEMATICAL
METHODS 2
24 lecture hours
5 ECTS credits
Sturm-Liouville theory
and expansion in orthogonal bases. Fourier and Laplace transforms. Partial Differential equations: Heat
equation, Wave equation, Laplace's equation. Spherical harmonics. Green's
functions for boundary value problems.Complex analysis up to Cauchy's
residue theorem.
THIRD YEAR BA SINGLE
HONOURS THEORETICAL PHYSICS COURSE
THIRD YEAR BA DOUBLE HONOURS MATHEMATICAL
PHYSICS COURSE
THIRD YEAR BA HONOURS MATHEMATICAL SCIENCE
COURSE
FOURTH YEAR COURSES
HONOURS COURSE
The modules for the final year Single Honours
course in Theoretical Physics and the Double Honours course in Mathematical
Physics are listed below.
For the Single Honours course in Theoretical
Physics students take all the listed modules. There
are 12 lectures and four tutorials per week. In
addition for one semester there are two hours laboratory work per week
and project work associated with module MP468. There
are 5 three hour written examination papers at the end of the second semester. Continuous assessment and project work associated with MP468 will count for up to 15% of the
fourth year mark in Theoretical Physics. The final
degree result will be based on 65% of the fourth year result plus 35%
of the third year result. The latter is applied
to the student's advantage.
Double Honours students in Mathematical Physics
take modules (a) MP462 and MP463 plus optional modules from the following
groups of modules which add up to 20 ECTS. (b)
MP460 and MP461 (10 ECTS), (c) MP464 and MP465 (10 ECTS), (d) MP466 and
MP467 (10 ECTS) and (e) MP468 and MP470 (20 ECTS). The final degree result in Mathematical Physics will
be based on 50% of the fourth year mark plus 50% of the third year mark. The latter is applied to the students advantage.
MP460 THERMODYNAMICS
24 lecture hours
5 ECTS credits
0th law of thermodynamics (definition
of temperature).
Ideal gas law, kinetic theory of
gases, Van der Waal's equation.
Maxwell-Boltzmann distribution.
1st law of thermodynamics.
2nd law of thermodynamics, (Carnot
cycles, entropy, Boltzmann's H-theorem).
3rd law of thermodynamics.
Thermodynamic functions (Helmholz
and Gibb's functions).
Legendre transforms (Gibb's surfaces,
Gibb's rule of phases, Gibbs-Duhem relation).
Maxwell's equations.
MP461 STATISTICAL
MECHANICS
24 lecture hours
5 ECTS credits
Partition functions (simple sub-systems,
ideal gas, simple solids, ferro-magnet, Ising
model). Micro-canonical and grand
canonical ensembles. Phase transitions and critical phenomena. Bose-Einstein
and Fermi-Dirac statistics. Bose-Einstein condensation (super-conductors and
super-fluids). Information theoretic approach to entropy and partition function.
MP462 QUANTUM MECHANICS
I
24 lecture hours
5 ECTS credits
Stern-Gerlach Experiments
Rotation of Basis States and Matrix
Mechanics
Angular Momentum
Time Evolution
A System of Two Spin-2 Particles.
Bell Inequalities.
MP463 QUANTUM MECHANICS
2
24 lecture hours
5 ECTS credits
Wave Mechanics in One Dimension
The One-Dimensional Harmonic Oscillator
Translational and Rotational Symmetry
in the Two-Body Problem
Bound States of Central Potentials
Perturbation Theory
MP464 SOLID STATE
PHYSICS
24 lecture hours
5 ECTS credits
Crystal Structure
Free Electron Theory of Metals
Energy Bands
Semiconductors
Diamagnetism and Paramagnetism
MP465 ELECTROMAGNETISM
24 lecture hours
5 ECTS credits
Review of Maxwell Equations in
vacuo
Scalar and vector potentials
Multipole expansions in electrostatics
Multipole expansions in magnetostatics
Dielectrics
Diamagnetism
and Paramagnetism
Maxwell's Equations in ponderable
media
Waveguides
Radiation from simple systems:
multipole expansions and energy transport
Co-variant formalism of electromagnetism,
gauge invariance
MP466 PARTICLE PHYSICS
24 lecture hours
5 ECTS credits
Introduction to Forces and Particles
The four forces; classification
of leptons, hadrons, mesons,
baryons; strangeness, gravitons
The Quark model:
Quark model of mesons and baryons;
charm (J/Psi); QCD;
asymptotic freedom
Electro-weak theory
Isospin; neutrinos; Higg's bosons;
electro-weak interactions;
neutrino masses
Symmetries
Conservation laws; discrete symmetries
(CPT); C, P and T violation
(K_L-K_S oscillations)
Grand Unification:
Grand unification; proton decay;
super-symmetry
Current developments:
Elementary discussion of string
theory, current topics
MP467 COSMOLOGY
24 lecture hours
5 ECTS credits
Star Formation:
Jean's mass; PP-chain and CNO-cycle.
Stellar Structure:
Hydro-static equilibrium; radiation
transport; Eddington limit
Degenerate Stars:
Super-novae; white dwarves; neutron
stars; pulsars; black-holes
Binary systems:
Gravitational radiation
Galactic structure and evolution:
Active galactic nuclei; radio
galaxies; quasars
Cosmology:
Big Bang; micro-wave background
radiation; cosmological constant;
nucleo-synthesis; inflation
Astro-particle physics:
Cosmic rays; monopoles; dark
matter
MP468 COMPUTATIONAL
PHYSICS II
12 lecture hours
+ 24 hours laboratory + 20 hours project work
12 ECTS credits
Partial Differential
Equations. Elliptic equations - Laplace's equation. Hyperbolic
equations
Wave equations. Parabolic equations - Diffusion. Conservative
methods - continuity
equation. Matrix eigenvalue problems - Schroedinger equation. Monte Carlo Methods and
Simulation - random
number generators, integration, Metropolis algorithm.
MP470 CHAOS, NONLINEAR
DYNAMICS & QUANTUM INFORMATION PROCESSING
36 lecture hours
8 ECTS credits
Fixed points, limit cycles and strange
attractors.
Iterated maps.
Quadratic maps: Period doubling,
Quasi periodicity, devil's staircase, Farey tree.
Universality. Intermittency route
to chaos.
Hamiltonian systems.
Lyapunov exponents, Kolmogorov-
Sinai entropy.Concept of Dimension. Fractals
and multifractals.
Fundamental Concepts of Quantum
Information processing.
Introduction to Quantum Mechanics
Introduction to computer science
Quantum Circuits
Quantum Fourier Transform and
its applications
Quantum search algorithm
Physical realisations of quantum
information processors
Ph.D. (Mathematical
Physics).
This is a course of study
ending in a substantial dissertation in a branch of Mathematical Physics,
making a significant original contribution to the subject. The research topic will be chosen from one of the areas
of expertise within the Department.
Research areas:
Relativistic quantum field theory, general relativity, quantum gravity,
renormalization group, gauge theory, application of topology in physics,
nonlinear physics, dynamical systems, classical and quantum chaos, low
dimensional systems, fractals, nonlinear-optics/photonics and computational
physics.
Minimum requirement II1 honours degree. (Normally a first class honours degree
is required.)
Three years full time.
Application forms may
be obtained from the Registrar's Office or directly from the Secretary of
the Department. Applicants should talk to the Head
or a member of the Department before applying.
No deadline, but it is
recommended that applications be submitted by June 30th.
M.Litt. / M.Sc. / Mathematical
Physics (Research Mode).
One can pursue a masters
degree in Mathematical Physics or Mathematical Science by research (dissertation)
or a combination of course work and research (lectures/dissertation).
Research areas:
Relativistic quantum field theory, general relativity, quantum gravity,
renormalization group, gauge theory, application of topology in physics,
nonlinear physics, dynamical systems, classical and quantum chaos, low
dimensional systems, fractals, nonlinear-optics/photonics and computational
physics.
Minimum requirement II1
honours degree.
Normally two years full
time.
Students who perform well
may, at the discretion of the Head of Department, transfer to the Ph.D
programme.
Application forms may
be obtained from the Registrar's Office or directly from the Secretary of
the Department. Applicants should talk to the Head
or a member of the Department before applying.
M.Sc. / M.A. / Mathematical
Physics/Mathematical Science (by examination).
Students take courses
in Mathematical Physics and/or Mathematics. The courses
taken by a student will be determined in consultation
with the Head of Department.
II2 Honours Degree.
Full time course.
Assessment is by continuous
assessment and written examination. Some of these
requirements may, in consultation with the head of Department, be satisfied
by the submission of a thesis on an area of Mathematical Physics or Mathematics.
Standard Honours classification
scheme.
Based on the performance
in the Degree, students may be allowed to proceed to study for a Ph.D.
subject to the availability of places and the approval of the Head of Department.
Higher Diploma in Mathematical Science
This one year course is intended for graduates holding a primary degree
in which mathematical physics formed a substantial part (for example, a
B.E., a B.A. (Gen) or B.Sc. (Gen) which included mathematical physics). It involves a course of lectures in Mathematical Physics,
together with a minor project whose emphasis is on the practical and modern
applications of the subject.
The Higher Diploma in
Mathematical Science is a one year full-time honours postgraduate diploma
course.
There are 12 lectures,
3 tutorials and 2 hours laboratory per week. Students
take modules MP350 (Classical Mechanics), MP354 (Computational Physics
I), MP361 (Mathematical Methods I), MP362 (Mathematical Methods 2), MP352
(Special Relativity), MP353 (Fluid Mechanics), and modules up to 30 ECTS
credits from MP460 (Thermodynamics), MP461 (Statistical Physics), MP462
(Quantum Mechanics I), MP463 (Quantum Mechanics 2), MP464 (Solid State Physics),
MP465 (Electromagnetism), MP466 (Particle Physics), MP467 (Cosmology), MP468 (Computational Physics
II), MP470 (Chaos, Nonlinear Dynamics and Quantum Information Processing).
In the examination period,
there are six three-hour examination papers. The
continuous assessment of the Computational Physics courses counts for up
to 15% of the overall degree mark.
The course involves extensive
computer simulation (modelling) of physical and engineering systems.
The course is open to
graduates holding a primary degree in which Mathematical Physics formed a
substantial component (e.g. B.Sc. (General) or B.A. (General) including Mathematical
Physics, or B.E.), subject to the approval of the Head of Department.
Candidates who obtain
a II1 honours may transfer to the M.Sc. programme subject to the
availability of places and the approval of the Head of Department.
Application forms may
be obtained from the Registrar's Office or directly from the Secretary of
the Department. Applicants should talk to the Head
or a member of the Department before applying.