CÓDE NAME OF MODULE TYPE MATHEMATICAL METHODS FOR NANOSCIENCE M M = mandatory E = elective 3.3.1. Learning goals of the module. (List the specific learning goals that the current module should provide to the student; goals can focus on content, skills, or attitudes) The goal of this module is to provide the students with the required fundamental mathematical methods for the theoretical developments of the degree. 3.3.2. Methodology: learning activities and credit value of the module (ECTS). 3.3.2.1. Learning activities. (Time required to teach the module; links to other modules included in the MSc Program and suggested chronological sequence with the latter) The program will consist of lectures up to 46 hours which are to be distributed among theoretical ones, seminars and problems. The instrumental character of the subject requires the dedication of a considerable number of seminars and practical exercises in order to apply the theoretical mathematical methods to real problems. Since this module is aimed to provide the student with basic knowledge, the subject will be held in the first term (four month period) of the first year of the degree. 3.3.2.2. ECTS credit value (and time) 1 ECTS credit = 25 hours UPV/EHU TYPE OF LECTURE Theory Practice M (2) S PA PL PO TA TAI PCL PCC Periodic Evaluation Final Classroom lectures 23 15 8 3 Personal work (3) 30 18 15 TOTAL 53 33 23 3 (1) M (standard lecture); S (seminar); PA (practical exercises in classroom); PL (practical exercises in laboratory); PO (practical exercises with computers); TA (non-industrial workshops); TAI (industrial workshops); PCL (clinical practice); PCC (field practice); the acronyms are taken from the Spanish wording. (2) M = maximum allowed is 60% of the full classroom lectures. (3) Personal work = time that the student would use to prepare and develop individual and group assignments. 1
3.3.2.3. Module Program. (Lectures) Lecture 1 THEORY OF FUNCTIONS OF A COMPLEX VARIABLE Lecture 2 INTEGRATION IN THE COMPLEX PLANE Lecture 3 FUNCTIONAL ANALYSIS. HILBERT SPACES Lecture 4 THEORY OF LINEAR OPERATORS. APPLICATIONS TO DIFFERENTIAL EQUATIONS. Lecture 5 GROUP THEORY 3.3.2.4. Bibliography. (Basic and specialized bibliographies, journal references, internet addresses, etc.) - COMPLEX ANALYSIS: FOR MATHEMATICS AND ENGINEERING. FIFTH EDITION, 2006. JOHN H. MATHEWS AND RUSSELL W. HOWELL - GRADUATE MATHEMATICAL PHYSICS. KELLY, JAMES J. - ANALISIS REAL Y COMPLEJO. W. RUDIN. MC GRAW HILL. - ADVANCED ENGINEERING MATHEMATICS. ERWING KREYZIG. JOHN WILEY&SONS - MATHEMATHICS METHODS FOR PHYSICS&ENGINEERING. RILEY ET AL. CAMBRIDGE - GROUP THEORY IN PHYSICS. J.F. CORNWELL 3.3.3. Criteria and methods for evaluation and grading (Analysis of the methodology that will be used to evaluate the learning process of the student) The evaluation of the knowledge of the fundamentals obtained by the student will be deduced by means of individual tasks which might include the resolution of practical problems and their presentation as a short lecture 2
3.3.4. Learning resources The student should be given open access to the bibliographical material of the libraries of the Faculty of Chemistry of the UPV/EHU, the Unit of Physics of Materials and also to that of the Donostia International Physics Center. Moreover, within the aim of performing computer practices and tasks the computer science resources of the Donostia International Physics Center will be also available. 3.3.5. Language and number of groups attending the module 1 NUMBER OF GROUPS x LANGUAGE: ENGLISH 3.3.6. Fields of science and technology to which the module is related CODE FIELD PHYSICS OF CONDENSED MATTER APPLIED PHYSICS 3.3.7. Department in charge of the Program CODE DEPARTMENT (1) DEPARTMENT OF MATERIALS PHYSICS 3.3.8. Teachers in charge of the module DNI Teacher UPV/EHU Number of credits 14.886.977 C Rivacoba Ochoa, Alberto 1 15.976.311 M Alvarez González, Fernando 1 3
CÓDE NAME OF MODULE TYPE FUNDAMENTALS OF QUANTUM MECHANICS M M = mandatory E = elective 3.3.1. Learning goals of the module. (List the specific learning goals that the current module should provide to the student; goals can focus on content, skills, or attitudes.) The laws of Quantum Mechanics are the laws that describe the phenomenon taking place at the nanoscale. This module is thought to address the fundamentals of quantum mechanics, i.e., the formalism from which quantum theory was built, as well as the basic physical problems that are only understood within this theory. The student will learn crucial concepts and tools, such as the probabilistic meaning of the wave function, the idea of operators and observables, the Schrödinger equation that describes the evolution of a system, and approximation methods that allow to solve the Schrödinger equation when the exact solution is not possible. 3.3.2. Methodology: learning activities and credit value of the module (ECTS). 3.3.2.1. Learning activities. (Time required to teach the module; links to other modules included in the MSc Program and suggested chronological sequence with the latter) The course consists of 45 hours of lectures and seminars. The course is offered for the first term and first year in Master program. The schedule takes into account that the central concepts and ideas given in this course are the basic background to other courses in the Master: Fundamentals in Solid State Physics Low dimensional systems and nanostructures Fundamentals of nanoscale characterization Nanostructural properties 3.3.2.2. ECTS credit value (and time) 1 ECTS credit = 25 hours UPV/EHU 4
TYPE OF LECTURE Theory Practice M (2) S PA PL PO TA TAI PCL PCC Periodic Evaluation Final Classroom lectures 25 20 3 Personal work (3) TOTAL 34.55 30 (4) M (standard lecture); S (seminar); PA (practical exercises in classroom); PL (practical exercises in laboratory); PO (practical exercises with computers); TA (non-industrial workshops); TAI (industrial workshops); PCL (clinical practice); PCC (field practice); the acronyms are taken from the Spanish wording. (5) M = maximum allowed is 60% of the full classroom lectures. (6) Personal work = time that the student would use to prepare and develop individual and group assignments. 3.3.2.3. Module Program. (Lectures) Lecture 1 THE ORIGINS OF QUANTUM THEORY Lecture 2 THE POSTULATES OF QUANTUM MECHANICS Lecture 3 OBSERVABLES: OPERATORS IN QUANTUM MECHANICS Lecture 4 POSITION AND MOMENTUM OPERATORS. UNCERTAINTY PRINCIPLE Lecture 5 SCHRÖDINGER EQUATION. STATIONARY STATES. TIME EVOLUTION OF QUANTUM SYSTEM Lecture 6 ONE-DIMENSIONAL PROBLEMS Lecture 7 THE ONE-DIMENSIONAL HARMONIC OSCILLATOR Lecture 8 GENERAL THEORY OF ANGULAR MOMENTUM 5
Lecture 9 ORBITAL ANGULAR MOMENTUM Lecture 10 SPIN ANGULAR MOMENTUM Lecture 11 PARTICLE IN A CENTRAL POTENTIAL. THE HYDROGEN ATOM Lecture 12 APPROXIMATION METHODS FOR STATIONARY AND TIME- DEPENDENT PROBLEMS Lecture 13 IDENTICAL PARTICLES: FERMIONS AND BOSONS Lecture 14 SCATTERING THEORY 3.3.2.4. Bibliography. (Basic and specialized bibliographies, journal references, internet addresses, etc.) - QUANTUM MECHANICS, C. COHEN TANNOUDJI, B. DIU, AND F. LALOË,, ED. JOHN WILEY AND SONS - MECÁNICA CUÁNTICA, F.J YNDURAIN ARIEL CIENCIA - QUANTUM MECHANICS, B.H. BRANSDEN AND C.J.JOACHAIN PEARSON EDUCATION - QUANTUM MECHANICS L. I. SCHIFF,, ED. MCGRAW-HILL - QUANTUM MECHANICS, A. MESSIAH, ED. DOVER - QUANTUM PHYSICS, R. EISBERG AND R. RESNICK, ED. JOHN WILEY AND SONS - QUANTUM MECHANICS (NON RELATIVISTIC THEORY), L. D. LANDAU AND E. M. LIFSHITZ, ED. BUTTERWORTH-HEINEMANN 6
3.3.3. Criteria and methods for evaluation and grading (Analysis of the methodology that will be used to evaluate the learning process of the student) The concepts of quantum mechanics are crucial to follow most of the modules given in this Master. For this reason, the method used to evaluate the learning process of the student will be a final exam that will represent 75% of the final grade. In this final exam the student will have the opportunity to show his/her familiarity with the basic concepts of quantum mechanics. The 25% of the grade left will evaluate the student s personal work. In particular, the student will be asked to solve a few problems related with the concepts explained during the lectures. 3.3.4. Learning resources The student will have access to the bibliographical resources available in the University of the Basque Country, Centro de Física de Materiales, and Donostia International Physics Center. 3.3.5. Language and number of groups attending the module 1 NUMBER OF GROUPS x LANGUAGE: ENGLISH 3.3.6. Fields of science and technology to which the module is related CODE FIELD PHYSICS OF CONDENSED MATTER APPLIED PHYSICS 3.3.9. Department in charge of the Program CODE DEPARTMENT (1) DEPARTMENT OF MATERIALS PHYSICS 7
3.3.10. Teachers in charge of the module DNI Teacher UPV/EHU Number of credits 0069057-X Andrés Arnau Pino 2.25 DNI Teacher other institutions Number of credits 16269816F Maite Alducin Ochoa 2.25 8
CÓDE NAME OF MODULE TYPE FUNDAMENTALS OF SOLID STATE PHYSICS M M = mandatory E = elective 3.3.1. Learning goals of the module. (List the specific learning goals that the current module should provide to the student; goals can focus on content, skills, or attitudes.) The gole of the module is to develop a generale picture of solid state physics that can be used by students to understand the classification of materials in terms of their properties: metals, semiconductors, and insulators. This includes general properties of crystal symmetry: crystal lattice translational symmetry and point group operations, reciprocal lattice, one particle properties and classification of one particle states in terms of wave vectors. It also includes band structure of metals, semiconductors, and insulators; vibrations in solids; experimental and theoretical methods of study of electronic and vibrational properties of solids. Magnetism of solids why some materials are magnetic? 3.3.2. Methodology: learning activities and credit value of the module (ECTS). 3.3.2.1. Learning activities. (Time required to teach the module; links to other modules included in the MSc Program and suggested chronological sequence with the latter) The course of the fundamentals of solid state physics will be given in the first four-month period of a master in nanoscience. This is because a knowledge of basic notions and properties of solids is fundamentals for understanding of other disciplines of a master in nanoscience. The themes of the course form a bridge that connects phenomena of Extended materials and Nano size metallic. Semiconductor and insulator systems. in particular, information obtained is necessary for study of other courses. 3.3.2.2. ECTS credit value (and time) 1 ECTS credit = 25 hours UPV/EHU TYPE OF LECTURE Theory Practice M (2) S PA PL PO TA TAI PCL PCC Periodic Evaluation Final Classroom lectures Personal work (3) TOTAL (7) M (standard lecture); S (seminar); PA (practical exercises in classroom); PL (practical exercises in laboratory); PO (practical exercises with computers); TA (non-industrial workshops); TAI 9
(industrial workshops); PCL (clinical practice); PCC (field practice); the acronyms are taken from the Spanish wording. (8) M = maximum allowed is 60% of the full classroom lectures. (9) Personal work = time that the student would use to prepare and develop individual and group assignments. 3.3.2.3. Module Program. (Lectures) Lecture 1 GEOMETRICAL DESCRIPTION OF CRYSTALS: DIRECT AND RECIPROCAL LATTICES. Lecture 2 VIBRATIONS IN SOLIDS: PHONONS Lecture 3 FREE ELECTRONS IN SOLIDS. Lecture 4 THE ELECTRONIC BANDSTRUCTURE OF SOLIDS: BLOCH THEOREM, THE NEARLY FREE-ELECTRON APPROXIMATION, THE THIGHT-BINDING APPROXIMATION. Lecture 5 BAND STRUCTURE OF SELECTED METALS Lecture 5 COHESION OF SOLIDS. Lecture 6 MAGNETISM IN SOLIDS: WHY SOME MATRERIOALS ARE MAGNETIC 3.3.5. Language and number of groups attending the module 1 x NUMBER OF GROUPS LANGUAGE: ENGLISH 10
3.3.6. Fields of science and technology to which the module is related CODE FIELD PHYSICS OF CONDENSED MATTER APPLIED PHYSICS 3.3.11. Department in charge of the Program CODE DEPARTMENT (1) DEPARTMENT OF MATERIALS PHYSICS 3.3.12. Teachers in charge of the module DNI Teacher UPV/EHU Number of credits Pedro Miguel Echenique Landiribar Eugene V. Tchulcov 11
CÓDE NAME OF MODULE TYPE CLASSICAL ELECTRODYNAMICS M M = mandatory E = elective 3.3.1. Learning goals of the module. (List the specific learning goals that the current module should provide to the student; goals can focus on content, skills, or attitudes.) The interaction among charges is the one that determines the structure of matter from the atomic level up to the formation of macroscopic structures. Furthermore, the interaction of the electromagnetic field with matter is the basis of a great number of techniques devoted to the analysis of the structure of the materials. In many problems classical electrodynamics provides an adequate description of the interactions in nanostructures. The aim of this subject is to familiarize the student with the basic concepts of electric and magnetic fields, the response of macroscopic systems to external fields, and the relation of this response with the microscopic structure of the medium. Moreover, based on the Maxwell equations the fundamental concepts of optics will be presented, and the propagation, reflexion and refraction of electromagnetic waves will be studied. 3.3.2. Methodology: learning activities and credit value of the module (ECTS). 3.3.2.1. Learning activities. (Time required to teach the module; links to other modules included in the MSc Program and suggested chronological sequence with the latter) The subject will consist in 45 hours of theoretical lectures and seminars. Since the aim of this subject is that the student adquires basic knowledges, the subject will be taught during the first quadrimester of the first year of the master. in this way the student will be able to apply in a sistematic way the adquired knowledge in the development of many subjects of the master, such as: Fundamental of solid state physics Low dimensional systems and nanostructures Fundamentals of nanoscale characterization Nanostructural properties 12
3.3.2.2. ECTS credit value (and time) 1 ECTS credit = 25 hours UPV/EHU TYPE OF LECTURE Theory Practice M (2) S PA PL PO TA TAI PCL PCC Periodic Evaluation Final Classroom lectures Personal work (3) TOTAL (10) M (standard lecture); S (seminar); PA (practical exercises in classroom); PL (practical exercises in laboratory); PO (practical exercises with computers); TA (non-industrial workshops); TAI (industrial workshops); PCL (clinical practice); PCC (field practice); the acronyms are taken from the Spanish wording. (11) M = maximum allowed is 60% of the full classroom lectures. (12) Personal work = time that the student would use to prepare and develop individual and group assignments. 3.3.2.3. Module Program. (Lectures) Lecture 1 INTRODUCTION TO ELECTROSTATICS. PROBLEMS OF ELECTROSTATICS WITH CONDUCTORS. Lecture 2 DIELECTRIC MEDIA. POLARIZATION. BOUNDARY CONDITIONS IN THE PRESENCE OF CONDUCTORS. ELECTROSTATIC ENERGY. Lecture 3 MAGNETOSTATICS. MAGNETIZATION. BOUNDARY PROBLEMS IN THE PRESENCE OF MAGNETIZABLE MEDIA. Lecture 4 FARADAY LAW. MAXWELL EQUATIONS. ENERGY OF THE ELECTROMAGNETIC FIELD. Lecture 5 ELECTROMAGNETIC WAVES. PROPAGATION. REFLEXION. REFRACTION. Lecture 6 RETARDED POTENTIALS. RADIATIVE SYSTEMS. RADIATION OF AN OSCILLATING DIPOLE. POTENTIALS CREATED BY A MOVING CHARGE. 13
3.3.2.4. Bibliography. (Basic and specialized bibliographies, journal references, internet addresses, etc.) - CLASSICAL ELECTRODYNAMICS, J. D. JACKSON, JOHN WILEY AND SONS, 1999 - CLASSICAL FIELD THEORY, F.E. LOW, JOHN WILEY AND SONS, 1997 - CLASSICAL THEORY OF ELECTROMAGNETISM, B. DI BARTOLO, WORLD SCIENTIFIC, 2004 - CLASSICAL ELECTRODYNAMICS, W. GRENIER, SPRINGER VERLAG, 1998. - PROPAGATION, SCATTERING AND DISSIPATION OF ELECTROMAGNETIC WAVES, A. S. ILYNSKI, G. YA. SLEPYAN, A. YA. SLEPYAN, PETER PETEGRINUS, 1993 -, THE FEYNMAN LECTURES ON PHYSICS: VOL. 2, R. P. FEYNMAN, R. B. LEIGHTON, AND M. SANDS, ADDISON-WESLEY, 2006. 3.3.5. Language and number of groups attending the module 1 NUMBER OF GROUPS x LANGUAGE: ENGLISH 3.3.6. Fields of science and technology to which the module is related CODE FIELD PHYSICS OF CONDENSED MATTER APPLIED PHYSICS 3.3.13. Department in charge of the Program CODE DEPARTMENT (1) DEPARTMENT OF MATERIALS PHYSICS 3.3.14. Teachers in charge of the module DNI Teacher UPV/EHU Number of credits Joseba Iñaki Juaristi Oliden Alberto Rivacoba Ochoa 14
CÓDE NAME OF MODULE TYPE INTRODUCTION TO MATERIAL SCIENCE M M = mandatory E = elective 3.3.1. Learning goals of the module. (List the specific learning goals that the current module should provide to the student; goals can focus on content, skills, or attitudes.) In this module we want the student to acquire a basic knowledge in materials science: a classification of materials depending on their structure and an overview and a description of thermal, mechanical optical, electric and magnetic properties of materials. The student must learn the importance of the different types of defects which change the properties of materials, like doping of semiconductors, and the structural changes appearing when submitting the materials to pressure, temperature or composition changes. Under the recent research results in materials science, a revision of the new methods for the design of new materials will be presented. 3.3.2. Methodology: learning activities and credit value of the module (ECTS). 3.3.2.1. Learning activities. (Time required to teach the module; links to other modules included in the MSc Program and suggested chronological sequence with the latter) The module will take 45 hours of lectures divided into theoretical ones and others more practical or applied like seminars. As it is a module where the student must acquire basic knowledge, it will be developed in the first half of the first course of the master. By this way the student will be capable to systematicallyapply these concepts on the development other modules in the master like: Fundamentals of solid state physics Low dimensional systems, and nanostructures Fundamentals of nanoscale characterization Nanostructural properties... 3.3.2.2. ECTS credit value (and time) 1 ECTS credit = 25 hours UPV/EHU TYPE OF LECTURE Theory Practice M (2) S PA PL PO TA TAI PCL PCC Periodic Evaluation Final Classroom lectures Personal work (3) TOTAL 15
(13) M (standard lecture); S (seminar); PA (practical exercises in classroom); PL (practical exercises in laboratory); PO (practical exercises with computers); TA (non-industrial workshops); TAI (industrial workshops); PCL (clinical practice); PCC (field practice); the acronyms are taken from the Spanish wording. (14) M = maximum allowed is 60% of the full classroom lectures. (15) Personal work = time that the student would use to prepare and develop individual and group assignments. 3.3.2.3. Module Program. (Lectures) Lecture 1 CLASSIFICATION OF MATERIALS :STRUCTURE AND FUNDAMENTAL PROPERTIES Lecture 2 IMPERFECTIONS: DEFECTS, DISLOCATION, IMPURITIES Lecture 3 MECHANICAL PROPERTIES Lecture 4 THERMAL PROPERTIES Lecture 5 OPTICAL PROPERTIES Lectura 6 ELECTRIC PROPERTIES Lectura 7 MAGNETIC PROPERTIES Lectura 8 DIFFERENT TYPE OF MATERIALS: POLYMERS, CERAMICS, ALLOYS, NEW MATERIALS. PREPARATION TECHNIQUES 3.3.2.4. Bibliography. (Basic and specialized bibliographies, journal references, internet addresses, etc.) - MATERIAL SCIENCE AND ENGINEERING: AN INTRODUCTION, WILLIAM D. CALLISTER, JR., ISBN-0471-73696-1 (WILEY). - PHYSICAL FOUNDATIONS OF MATERIALS SCIENCE, G. GOTTSTEIN ISBN 3-540-40139-3 (SPRINGER) 16
3.3.3. Criteria and methods for evaluation and grading (Analysis of the methodology that will be used to evaluate the learning process of the student) As it is a module of fundamental and basic character for the development of the master, it will be necessary to evaluate the acquired knowledge by means of an examination which will correspond to a 50% of the final qualification. The resting 50% will be marked by the exposure of a subject related to the matter and the corresponding exposition of it. 3.3.4. Learning resources The student will have free access to the libraries of the Facultad de Química of the UPV/EHU, the Unidad de Física de Materiales (Centro Mixto CSIC-UPV/EHU) and to the existing computer resources. 3.3.5. Language and number of groups attending the module 1 NUMBER OF GROUPS x LANGUAGE: ENGLISH 3.3.6. Fields of science and technology to which the module is related CODE FIELD PHYSICS OF CONDENSED MATTER APPLIED PHYSICS 3.3.15. Department in charge of the Program CODE DEPARTMENT (1) DEPARTMENT OF MATERIALS PHYSICS 3.3.16. Teachers in charge of the module DNI Teacher UPV/EHU Number of credits 15919409M Juan José del Val Altunas 2.5 Julián María González Estévez 2 17