Advanced Studies in Physics – THEMATIC UNITS

PSF50: ADVANCED STUDIES IN CLASSICAL PHYSICS

Module code: PSF50

ECTS Credit Points: 20

Module Type: Compulsory

Year: 1^st

Language: Greek

Module Outline

Module General Description: The T.U. aims to cover at the postgraduate level the fundamental “classical”, i.e., non-quantum, theories, in particular Classical (Newtonian) Mechanics, as expressed by Lagrange, Hamilton, etc., and Maxwell’s Classical Electrodynamics. The vast majority of macroscopic physical phenomena may be described by the laws in the aforementioned classical structure. However, even the description of microscopic phenomena based on Quantum Theory is impossible save through a “classic analog” (system). Thus, the quantum mechanical description of any physics system requires sound knowledge of Classical Mechanics and Electrodynamics. It must be noted that Classical Electrodynamics, i.e. the theory of macroscopic electromagnetic phenomena, also includes the Special Theory of Relativity. Only large-scale gravitational phenomena, which are described in the General Theory of Relativity, are not included in the aforementioned diptych, which offers a concise description of physical phenomena at macroscopic distances.

Learning Outcomes: The successful completion of PSF50 aims at the following scientific objectives:

• Ability to formulate equations of motion of physical systems through Principles of Change
• Knowledge and comprehensive understanding of the time evolution of physical systems in configuration space through the solving of the corresponding Lagrange equations
• Knowledge and comprehensive understanding of the time evolution of physical systems in phase space through the solving of the Hamilton equations and/or through the formalism of Poisson curves.
• Knowledge and comprehensive understanding of the issues of small oscillations (Normal Modes).
• Ability to formulate Lagrange and Hamilton formalisms for Continuum Mechanics and Classical Field Theory systems.
• Ability to formulate Maxwell’s equations for electrodynamics and their solution in various macroscopic systems.
• Knowledge of the emission and absorption of Electromagnetic Waves.
• Knowledge and comprehensive understanding of the electromagnetic properties of physical systems of Conductors, Dielectrics, and Materials with Magnetic Properties.
• Formulation and solution of the kinematics and electromagnetic behavior of physical systems in the context of the Special Theory of Relativity.
• Knowledge and comprehensive understanding of radiation phenomena of accelerated electric charges.

Subjects covered:

• Advanced Studies in Classical Mechanics
• Advanced Studies in Classical Electromagnetism

Prerequisites: There are no prerequisite courses.

Evaluation: Students are assigned to submit six (6) written assignments during the academic year. The average grade of the six (6) written assignments, weighted at 30%, is taken into consideration for the calculation of the final grade. The grade of written assignments is activated only with a score equal to or above the pass level (≥5) in the final or resit exams.

The grade of the final or the resit exams shall be weighted at 70 % for the calculation of the final grade.

PSF51: MATHEMATICAL METHODS FOR PHYSICS

Module code: PSF51

ECTS Credit Points: 20

Module Type: Compulsory

Year: 1^st

Language: Greek

Module Outline

Module General Description: Physics as a science acquired substantially changed as it began to use Mathematics already a few centuries ago as its main tool. In modern times, this relationship has strengthened so much that all serious attempt to solve physical problems cannot be understood without the use of Mathematics, but it has also evolved to the point that it acquired a two-way character. According to these considerations, the purpose of module is for the student to acquire the necessary basic knowledge in various areas of Mathematics and to learn how to apply the relevant methods to solve physical problems.

In detail, the content of the module is:

• Differential equations: classification into linear and non-linear, as well as ordinary and partial differential equations. Methods of solving linear differential equations, with constant and non-coefficients (emphasis on second order). Smooth and non-smooth points, applications to physical systems.
• Complex analysis and applications in the calculation of integrals and infinite sums.
• Special functions and orthogonal polynomials. Expansion in eigenfunctions. Laplace, diffusion, Helmholtz, Poisson equations
• Green’s functions: Construction of Green’s functions for the Helmholtz, Poisson, Laplace equations and for the wave equation.
• Problems in Cartesian, spherical and cylindrical coordinates with homogeneous and inhomogeneous boundary conditions. Expansion in orthogonal polynomials.
• Boundary and initial condition problems.
• Calculus of changes and physical applications.
• Probability theory and experimental data analysis. Applications to physics problems.

Learning Outcomes: Students who successfully complete this module unit will be able to analyze and model natural processes and phenomena with advanced mathematical methods and produce analytical results in several cases. More specifically, students will be able to:

• use basic elements of complex analysis to calculate integrals and infinite series
• solve second-order ordinary differential equations, which often appear in physics, using special functions whose properties are also thoroughly studied
• apply integral transformations to solve physics problems
• use special functions, the method of separation of variables and appropriate coordinate systems to solve partial differential equations that arise in boundary and initial condition problems
• solve physics problems using Green’s functions
• formulate physical problems as transformation problems and produce analytical solutions
• know probability theory, calculate the probability distributions of random variables and their functions, and analyze experimental data.

Subjects covered:

• Mathematical Methods in Physics
• Mathematical Methods of Experimental Data Analysis

Prerequisites: There are no prerequisite courses.

Evaluation: Students are assigned to submit six (6) written assignments during the academic year. The average grade of the six (6) written assignments, weighted at 30%, is taken into consideration for the calculation of the final grade. The grade of written assignments is activated only with a score equal to or above the pass level (≥5) in the final or resit exams.

The grade of the final or the resit exams shall be weighted at 70 % for the calculation of the final grade.

PSF60: ADVANCED STUDIES IN QUANTUM PHYSICS

Module code: PSF60

ECTS Credit Points: 20

Module Type: Compulsory

Year: 1^st

Language: Greek

Module Outline

Module General Description: The aim of the module is the development at the postgraduate level of the fundamental principles, methods, and applications of non-relativistic quantum mechanics with the use of techniques borrowed from linear algebra, operator theory and differential equations in order to solve problems in the field of study of quantum theory.

Quantum mechanics is the only existing theoretical framework for the study and interpretation of the entirety of the physical processes that occur at the microscopic level. As such, it occupies a prominent position in modern physics and is one of the greatest scientific advances of the twentieth century. PSF60 focuses exclusively on the subject matter of non-relativistic quantum physics which occurs based on the principle of correspondence, from non-relativistic classical mechanics. This theory is successfully used to describe physical phenomena in the field of (relatively) low energies. High energies require the generalization of the theory in relativistic quantum mechanics, which occurs correspondingly from classical relativistic mechanics, but is not part of the syllabus. The methodology developed in the lessons is based on linear algebra, operator theory, and differential equations that serve the solution requirements of physical problems, as appropriate, but also the mathematical foundation of quantum theory. Problems with exact solutions are described in detail based on the mathematical theory of special functions, while for the rest, approximate solution methods are introduced and applied (perturbation method, etc.). A crucial aspect of quantum mechanics are symmetries, wherever they exist, and representations of their operators. Physical problems are split into two basic categories: bound state problems and scattering problems, for which the corresponding solution techniques are taught. The primary applications of non-relativistic quantum mechanics concern problems of atomic and molecular physics, quantum optics, quantum chemistry, nuclear physics and solid-state physics, the latter of which exhibits numerous technological applications in everyday life. High-energy processes, such as those found in elementary particle physics, can only be explained by relativistic quantum mechanics and quantum field theory.

All the laws that govern the microcosm are drawn from the basic principles of quantum physics discussed in PSF60.

Detailed Descritpion:

• Schrödinger equation – background: the wavefunction, Introductory mathematical notions, the postulates of quantum mechanics, Heisenberg inequalities.
• Simple quantum Systems: harmonic oscillator-coherent states, one dimensional bound state and scattering problems.
• Mathematical formalism of quantum theory: vector spaces, abstract Hilbert spaces, operators on Hilbert spaces, Operators-eigenvalues and eigenstates, Position and Momentum representations of wavefunctions and operators.
• Quantum theory in three dimensions: rotations and angular momentum.
• Schrodinger equation in three dimensions, spherically symmetric potentials, examples and applications, the Hydrogen atom.
• The dynamics of a quantum particle, propagator, Feynman path integrals, density operator.
• Spin, Symmetries, Spherical symmetry, symmetry groups and their representations, angular momentum addition, reflections, parity, time reversal, local gauge symmetry.
• Identical particles.
• Time dependent perturbation theory.
• Scattering: fundamental notions, general theory, scattering matrix, scattering states, scattering for spherically symmetric potentials.

Learning Outcomes: Upon successful completion of PSF60, students will be able to:

• understand how to apply the laws of quantum physics to the real world.
• acquire the technical skills to solve complex problems.
• analyze a variety of exactly solvable trap and scattering problems
• develop and applies approximate methods to study systems of atomic, molecular, nuclear physics and solid state physics.
• compare theoretical predictions with experimental results.
• evaluate modern results (as analyzed in published scientific articles) based on a broad knowledge of the fundamental laws of quantum physics.

Subjects covered:

• Quantum Mechanics
• Quantum Chemistry

Prerequisites: There are no prerequisite courses.

Evaluation: Students are assigned to submit six (6) written assignments during the academic year. The average grade of the six (6) written assignments, weighted at 30%, is taken into consideration for the calculation of the final grade. The grade of written assignments is activated only with a score equal to or above the pass level (≥5) in the final or resit exams.

The grade of the final or the resit exams shall be weighted at 70 % for the calculation of the final grade.

PSF61: STRUCTURE OF MATTER AND UNIVERSE

Module code: PSF61

ECTS Credit Points: 20

Module Type: Optional

Year: 2^nd

Language: Greek

Module Outline

Module General Description: The main objective of this unit is for the student to deepen his/her knowledge and connect the structure of matter from its most elementary form to the cosmological moment when gravity prevails and small and large star systems are being formed (stars, planets, galaxies, etc.). The theoretical background and mathematical tools of these sciences (eg. elementary particle physics, theoretical cosmology, astrophysics, observational cosmology) are used in an attempt to describe physically and mathematically the evolutionary path from Big Bang to large-scale structures, the connection between the micro and macro – scales of the cosmos.

Learning Outcomes: After completing module PSF 61 students will,

• Possess advanced knowledge in Solid-State Physics, Particle Physics, and Quantum Field Theories, and in particular Degree Theories and Astrophysical Cosmology.
• Understand and distinguish the common foundation of all these different fields of physics that describe the microcosm and the macrocosm by combining this knowledge.
• Learn to focus on the syllabus with critical thinking and categorize each piece of knowledge they are taught, given that they are required to cover a very large and diverse material.
• Gradually understand the discovery of the common foundation of the different fields of physics through the analysis and synthesis of different knowledge.
• Reorganize what they learned at the undergraduate level as a science student, laying a solid foundation for their scientific thinking, through the organization and synthesis of the different knowledge.
• Having changed their way of thinking, along with the new knowledge they will have acquired together with their comprehensive understanding of it, students will be able to draw conclusions about the world around them and transfer the skills they have acquired and their judgement to other situations in their lives.

Subjects covered:

• Elementary Particles
• Nuclei
• Solids
• Astrophysics

Prerequisites: There are no prerequisite courses.

Evaluation: Students are assigned to submit six (6) written assignments during the academic year. The average grade of the six (6) written assignments, weighted at 30%, is taken into consideration for the calculation of the final grade. The grade of written assignments is activated only with a score equal to or above the pass level (≥5) in the final or resit exams.

The grade of the final or the resit exams shall be weighted at 70 % for the calculation of the final grade.

PSF62: MATERIALS AND DEVICES SCIENCE

Module code: PSF62

ECTS Credit Points: 20

Module Type: Optional

Year: 2^nd

Language: Greek

Module Outline

Module General Description: PSF62 aims to discuss and acquaint students with the fundamental electric, optical, structural, and electronic properties of various classes of Advanced Materials, in addition to the basic physical principles that govern and determine the functionality of various Optoelectronic and Photonic Devices as well as Microelectronics Devices used in modern applications based on the properties of these materials. The unit also aims to teach students the strong correlation between the properties of materials and the function and characteristics of devices. Categories of materials covered in the syllabus are Metals, Semiconductors, Polymers, Magnetic Materials, and Superconductors, and the devices in which these materials are used with applications in power and light generation and electronic applications are p-n contacts, electronic diodes, light-emitting diodes and photodiodes/photodetectors, bipolar contact and field effect transistors, solar cells, lasers, and (micro)sensors.

Learning Outcomes: PSF62 generally aims to provide in-depth knowledge to students of the postgraduate program “Advanced Studies in Physics” regarding both the Physics of various categories of Materials, and the Physics of Optoelectronics and Photonic Devices in addition to Microelectronic Devices used in modern applications whose function depends on the properties of the aforementioned Materials.

The T.U. aims to provide general and specialized knowledge in the field of Materials and Devices Science. The knowledge focuses

• on the understanding of the behavior of electrons within solid materials and how this behavior categorizes said materials into metals, semiconductors, and insulators,
• the study of the basic manufacturing and characterization processes and fundamental physico-chemical properties of different classes of materials such as Metals, Semiconductors, Polymers, Magnetic and Ceramic Materials, and
• their applications in various categories of Photonic and Optoelectronic Structures and Devices as well as Microelectronics Devices, such as p-n contacts, electronic diodes, light-emitting diodes and photodiodes/photodetectors, bipolar contact and field effect transistors, solar cells, lasers, and (micro)sensors, in order to analyze in detail their principles of function.

A primary objective of the T.U. is for students to understand the most important optoelectronic and structural properties of the materials in the syllabus and the basic physical and functional principles of the aforementioned devices.

Upon successful completion of PSF62, postgraduate students are expected to possess in-depth knowledge of the properties of these categories of Materials as well as the Physics and functional principles that govern their modern applications in Structures and Devices, mainly in the field of Optoelectronics/Photonics and Energy.

Subjects covered:

• Metals – Semiconductors
• Microelectronics
• Sensors and Biosensors
• Laser Beams – Optoelectronics
• Materials Science
• Polymer Science

Prerequisites: There are no prerequisite courses.

Evaluation: Students are assigned to submit six (6) written assignments during the academic year. The average grade of the six (6) written assignments, weighted at 30%, is taken into consideration for the calculation of the final grade. The grade of written assignments is activated only with a score equal to or above the pass level (≥5) in the final or resit exams.

The grade of the final or the resit exams shall be weighted at 70 % for the calculation of the final grade.

PSFDE: THESIS

Module code: PSFDE

ECTS Credit Points: 40

Module Type: Compulsory

Year: 2^nd

Language: Greek

Module Outline

General Description: The research objects utilized in writing a thesis are harmoniously integrated into the main orientations of the program, that is, understanding the structure of Matter and the Universe and the Material Sciences and Devices.

The director of the program selects groups of related subjects, on the basis of which the prospective students submit a relevant proposal for elaboration. Subsequently, the Board of Directors (and correspondingly as above) designates the supervising member (First supervisor) and the second member of the Evaluation Committee for each submitted MDE proposal if it meets the basic academic requirements. Then the first Supervisor, in collaboration with the students, finalizes the topic and the basic content of the MDE in the digital education area within the first month of preparation and gives the final approval.

Thesis subjects may be changed within the first month of writing. In such a case, the relevant request is submitted for approval to the S.P. Director, together with the necessary documentation, by the 1st Supervisor, with notification to the second member of the Examination Committee. In case of approval, the relevant administrative body must be informed.

In particular, the General Categories of subjects for the Master’s Thesis are, presently, the following:

• Quantum Field Theory – Elementary Particle Physics
• Classical Field Theory – Solitons
• Condensed Matter Physics
• Gravity – General Theory of Relativity
• Cosmology
• Astrophysics
• Astroparticle Physics
• Experimental Physics of Elementary Particles
• Biophysics

The theory and practice used to further deepen the student’s knowledge is based to some extent on the materials modules.

However, for further deepening and acquisition of specialized knowledge and skills, the student, in collaboration with the supervisor, studies work from the relevant literature. This process usually takes 2-3 months. Then the thesis prepared and is checked in its stages both by the supervisor and by a second evaluator.

Learning Outcomes: The students who will successfully complete the module:

• they will have obtained a deep knowledge of the subject of their subject to the extent that they will be able to comfortably and fluently read and acquire information on cutting-edge research topics from publications in research journals of the respective research area.
• They will be able to give high level seminars in which they will be able to explain their subject clearly and to answer related questions from other scientists.

General Regulation for Preparing Graduate Dissertations in PC with an annual Module Correspondence

For more information regarding the Specifications – Useful Material for writing Master’s Theses and uploading a Thesis at the H.O.U. Repository, you can go to the Digital Training Area http://study.eap.gr and especially to the Program of Studies section.

Prerequisites: The presentation of the Thesis takes place after the successful completion of the program’s Course Modules.