FUNDAMENTALS OF THEORETICAL PHYSICS

Fisica FUNDAMENTALS OF THEORETICAL PHYSICS

0512600013
DIPARTIMENTO DI FISICA "E.R. CAIANIELLO"
EQF6
PHYSICS
2020/2021

OBBLIGATORIO
YEAR OF COURSE 3
YEAR OF DIDACTIC SYSTEM 2017
PRIMO SEMESTRE
CFUHOURSACTIVITY
972LESSONS
336EXERCISES
Objectives
KNOWLEDGE AND UNDERSTANDING:
CONSOLIDATION OF KNOWLEDGE OF MACRO-PHYSICS AND UNDERSTANDING OF THE MICRO-PHYSICS, WITH SPECIAL ATTENTION TO THE RELATIVISTIC MECHANICS AND QUANTUM MECHANICS. KNOWLEDGE OF ADVANCED TOPICS IN THE FIELD OF QUANTUM PHYSICS.

APPLYING KNOWLEDGE AND UNDERSTANDING:
ABILITY TO APPLY THE ACQUIRED KNOWLEDGE IN DIFFERENT CONTEXTS, AND TO PERCEIVE THE INTERDISCIPLINARY VALUE OF RELATIVISTIC MECHANICS AND QUANTUM MECHANICS AND THE METHODOLOGIES OF THESE DISCIPLINES; THE ABILITY TO DEVELOP SIMPLE MODELS FOR THE DESCRIPTION OF ATOMIC PHENOMENA; APPLICATION OF BASIC CONCEPTS OF RELATIVISTIC AND QUANTUM MECHANICS TO THE STUDY OF FRONTIER PROBLEMS IN THIS FIELD.
Prerequisites
1)MATHEMATICAL SKILLS
MATRIX ALGEBRA: SYMMETRIC MATRICES; ORTHOGONAL MATRICES; HERMITIAN MATRICES; UNITARY MATRICES; DIAGONALIZATION OF MATRICES; EIGENVALUES AND EIGENVECTORS. VECTOR SPACES. SCALAR PRODUCT IN FUNCTIONAL SPACES. INTEGRATION. COMPLEX NUMBERS AND ELEMENTS OF COMPLEX ANALYSIS.
2) PHYSICAL SKILLS
CLASSICAL MECHANICS; ANALYTICAL MECHANICS; ELECTROMAGNETISM; OPTICS.
Contents
CRISIS OF CLASSICAL PHYSICS (10 HOURS)
MICHELSON AND MORLEY EXPERIMENT; BLACK BODY SPECTRUM; PHOTOELECTRIC EFFECT AND COMPTON EFFECT; ELECTRON DIFFRACTION; DE BROGLIE'S RELATIONSHIP; RUTHERFORD EXPERIMENT AND ATOMIC SPECTRA; STERN AND GERLACH EXPERIMENT; WAVES AND PARTICLES; INTERFERENCE EXPERIMENTS.

SPECIAL RELATIVITY (24 HOURS)
LORENTZ TRANSFORMATIONS. INTRODUCTION TO TENSORS. RELATIVISTIC KINEMATICS. RELATIVISTIC DYNAMICS. RELATIVISTIC SCATTERING. COVARIANT FORMULATION OF THE ELECTROMAGNETIC FIELD. ELECTROMAGNETIC FIELD TENSOR. LORENTZ INVARIANTS AND LORENTZ GROUP.

MATHEMATICAL BASES OF QUANTUM MECHANICS (10 HOURS)
PROBABILITY AND PROBABILITY AMPLITUDES. UNCERTAINTY PRINCIPLE. LINEAR OPERATORS. MATRIX REPRESENTATIONS. COMPLETENESS RELATIONSHIP PRODUCT OF OPERATORS. BASIS CHANGES AND UNITARY TRANSFORMATIONS. SCALAR PRODUCT. THE CONCEPT OF MEASUREMENT IN QUANTUM MECHANICS. MEASUREMENTS AND OBSERVABLES. EXPECTATION VALUES OF OBSERVABLES. EIGENVALUES AND EIGENVECTORS OF OBSERVABLES. EIGENVECTORS OF OBSERVABLES AS BASIS VECTORS. COMPATIBLE AND INCOMPATIBLE OBSERVABLES. UNCERTANTYHEISENBERG PRINCIPLE. POSITION OPERATOR. MOMENTUM OPERATOR. CANONICAL COMMUTATOR RULES.

SCHROEDINGER EQUATION (8 HOURS)
HAMILTONIAN OPERATOR. TIME DEPENDENT STATES. CURRENT DENSITY AND CONTINUITY EQUATION. SYMMETRIES AND CONSERVATION LAWS. DERIVATIVE OF AN OPERATOR WITH RESPECT TO TIME. CONSERVED QUANTITIES. EHRENFEST THEOREM. STATIONARY STATES. SCHROEDINGER EQUATION FOR STATIONARY STATES. PARITY. EIGENVALUES AND EIGENSTATES OF THE PARITY OPERATOR. SYMMETRY FOR SPATIAL INVERSION AND CONSERVATION OF PARITY.

ONE-DIMENSIONAL PROBLEMS (12 HOURS)
GENERAL PROPERTIES OF THE SCHROEDINGER EQUATION. INFINITE WELL POTENTIAL AND FINITE POTENTIAL. POTENTIAL STEP. TRANSMISSION AND REFLECTION COEFFICIENTS. POTENTIAL BARRIER. TUNNEL EFFECT. DELTA POTENTIALS. HARMONIC OSCILLATOR. DIRAC'S OPERATOR METHOD FOR THE SOLUTION OF THE SCHROEDINGER EQUATION OF THE HARMONIC OSCILLATOR.

GENERAL THEORY OF ANGULAR MOMENTUM (8 HOURS)
ANALYTICAL SOLUTION AND ALGEBRAIC SOLUTION OF THE EIGENVALUE EQUATION FOR THE ANGULAR MOMENTUM OPERATOR. EIGENVALUES AND EIGENVECTORS OF THE ANGULAR MOMENTUM OPERATOR. ORBITAL ANGULAR MOMENTUM AND SPIN ANGULAR MOMENTUM. COMPOSITION OF ANGULAR MOMENTS. CLEBSCH-GORDAN COEFFICIENTS.

MOTION IN A CENTRAL FIELD (10 HOURS)
COULOMBIAN FIELD. HYDROGEN ATOM. EIGENVALUES AND EIGENFUNCTIONS OF THE DISCRETE SPECTRUM. CALCULATION OF AVERAGE VALUES OF DIFFERENT PHYSICAL QUANTITIES IN THE STATES OF A HYDROGENIC ATOM. SCHRODINGER EQUATION FOR A HYDROGENOID ATOM WITH ELECTROMAGNETIC RADIATION.

APPROXIMATION METHODS (16 HOURS)
TIME DEPENDENT AND INDEPENDENT PERTURBATION THEORY. NON DEGENERATE CASE AND DEGENERATE CASE. VARIATIONAL METHOD. APPLICATIONS. FINE STRUCTURE CORRECTIONS. RELATIVISTIC CORRECTIONS TO KINETIC ENERGY, SPIN-ORBIT COUPLING AND DARWIN'S TERM. ZEEMAN EFFECT. PASCHEN-BACK EFFECT. LINEAR AND SQUARED STARK EFFECT. ABSORPTION AND EMISSION RADIATION. DIPOLE APPROXIMATION. SELECTION RULES.

MODERN QUANTUM MECHANICS (10 HOURS)
EPR PARADOX. BELL INEQUALITY. EXPERIMENTAL TESTS. CLONING THEOREM. QUANTUM TELEPORTATION. ELEMENTS OF QUANTUM CRYPTOGRAPHY.

Teaching Methods
THE TEACHING INCLUDES 108 HOURS OF CLASSROOM TEACHING, BETWEEN LESSONS AND EXERCISES (12 CREDITS). IN PARTICULAR, 72 HOURS OF LESSONS (9 CREDITS) AND 36 HOURS OF EXERCISES (3 CREDITS) ARE FORESEEN.
THEORETICAL LESSONS PRESENT THE TOPICS FOLLOWING THE HISTORICAL DEVELOPMENT OF THE DISCIPLINE. THE EXERCISES DISCUSS PROBLEMS TO BE SOLVED USING THE TECHNIQUES PRESENTED IN THE THEORETICAL LESSONS, WITH INCREASING COMPLEXITY. THE SOLUTION OF THE PROBLEM IS GUIDED BY THE TEACHER AND TENDS TO DEVELOP AND STRENGTHEN THE ABILITY TO IDENTIFY THE MOST SUITABLE TECHNIQUES FOR SOLVING THE EXERCISE. THE ATTENDANCE OF THE COURSE, ALTHOUGH NOT MANDATORY, IS STRONGLY RECOMMENDED, ESPECIALLY FOR WHAT CONCERNS THE EXERCISES.
THE STUDENT MAY USE THE E-LEARNING PLATFORM SPECIFICALLY DESIGNED TO DOWNLOAD TEACHING MATERIALS (PROBLEMS AND REFERENCE TEXTS) AND TO INQUIRE ABOUT THE TOPICS COVERED IN CLASS.

Verification of learning
THE ACHIEVEMENT OF THE TEACHING OBJECTIVES IS CERTIFIED BY PASSING AN EXAM WITH A NUMERICAL ASSESSMENT UP TO 30/30.
THE EXAM INVOLVES A WRITTEN AND AN ORAL TEST, BOTH OF WHICH ARE EVALUATED UP TO 30/30. TO TAKE PART TO THE ORAL EXAM, THE STUDENT MUST PASS THE WRITTEN TEST WITH A MINIMUM SCORE OF 18/30. DURING THE LECTURES IT IS SCHEDULED A PARTIAL WRITTEN TEST. THIS PARTIAL TEST CONCERNS ONLY SPECIAL RELATIVITY TOPICS AND IT IS EVALUATED UP TO 30/30. THE TEST REQUIRES THE SOLUTION OF OPEN-ENDED QUESTIONS AND MULTIPLE-ANSWER QUESTIONS. IF THE SCORE IS GREATER THAN OR EQUAL TO 18/30, THE STUDENT CAN BE CONSIDERED EXEMPTED FROM SOLVING THE RELATIVITY EXERCISE PRESENT IN THE WRITTEN TESTS OF THE EXAMS, AND WILL NOT DISCUSS SPECIAL RELATIVITY TOPICS AT THE ORAL EXAM. THE FINAL SCORE ATTRIBUTED TO THE WRITTEN TEST WILL BE GIVEN BY THE AVERAGE OF THE MARKS OF THE EXEMPTION TEST AND OF THE QUANTUM MECHANICS EXERCISE OF THE WRITTEN EXAM.
THE WRITTEN TEST, AIMED AT VERIFYING THE LEVEL OF UNDERSTANDING OF THE TOPICS COVERED IN THE LESSONS, CONSISTS IN THE SOLUTION OF TWO PROBLEMS, ONE OF SPECIAL RELATIVITY AND ONE OF QUANTUM MECHANICS. THE TIME ALLOCATED FOR THE WRITTEN TEST IS NINETY MINUTES, IF THE STUDENT HAS PASSED THE EXEMPTION TEST, AND TWO HOURS, IN THE OTHER CASES.
THE EVALUATION OF THE ORAL TEST WILL TAKE INTO ACCOUNT THE ABILITY TO IDENTIFY THE MOST APPROPRIATE STRATEGIES FOR ANALYZING THE COURSE TOPICS, THE ABILITY TO CLEARLY AND CONCISELY PRESENT THE OBJECTIVES, THE PROCEDURE AND THE RESULTS OF THE TOPICS OF THE LECTURES, AS WELL AS THE ABILITY TO DEEPEN THE TOPICS TREATED, ORIENTING THEMSELVES APPROPRIATELY BETWEEN THE PROPOSED MATERIALS.
THE MINIMUM ASSESSMENT LEVEL (18/30) IS ATTRIBUTED WHEN THE STUDENT DEMONSTRATES UNCERTAINTIES IN THE APPLICATION OF THE FOUNDATIONAL CONCEPTS OF RELATIVISTIC MECHANICS AND QUANTUM MECHANICS, HIGHLIGHTING A LIMITED KNOWLEDGE OF THE MAIN TECHNIQUES AND METHODOLOGIES OF MODERN PHYSICS.
THE MAXIMUM LEVEL (30/30) IS ATTRIBUTED WHEN THE STUDENT DEMONSTRATES A COMPLETE AND IN-DEPTH KNOWLEDGE OF THE CONCEPTS AND METHODS OF MODERN PHYSICS AND SHOWS A REMARKABLE ABILITY TO CONNECT AND PROPERLY EXPOSE THE DIFFERENT TOPICS.
THE FINAL MARK, EXPRESSED IN THIRTIETHS WITH POSSIBLE HONORS, IS OBTAINED AS THE AVERAGE OF THE TWRITTEN AND THE ORAL EXAMINATIOS. THE HONOR IS AWARDED WHEN THE CANDIDATE DEMONSTRATES SIGNIFICANT KNOWLEDGE OF THE THEORETICAL CONTENTS AND SHOWS HIS ABILITY TO PRESENT THE TOPICS WITH SIGNIFICANT LANGUAGE PROPERTIES AND AUTONOMOUS PROCESSING CAPACITY, EVEN IN CONTEXTS OTHER THAN THOSE PROPOSED BY THE TEACHER.

Texts
MANDATORY BOOKS
C. NOCE INTRODUZIONE ALLA FISICA MODERNA ARACNE EDITRICE
C. NOCE MODERN PHYSICS IOP PUBLISHING
R. RESNICK INTRODUZIONE ALLA RELATIVITÀ RISTRETTA CEA AMBROSIANA
W. RINDLER INTRODUCTION TO SPECIAL RELATIVITY CLARENDON
J. D. JACKSON CLASSICAL ELECTRODYNAMICS WILEY & SONS
D. J. GRIFFITHS INTRODUZIONE ALLA MECCANICA QUANTISTICA CEA AMBROSIANA
C. COHEN-TANNOUDJI, B. DIU, F. LALOE QUANTUM MECHANICS I & II WILEY & SONS
R. ROSSETTI ISTITUZIONI DI FISICA TEORICA LEVROTTO E BELLA
C. ROSSETTI ESERCIZI DI MECCANICA QUANTISTICA ELEMENTARE LEVROTTO E BELLA
OTHER SUGGESTED BOOKS
D. HALLIDAY, R. RESNIK, J. WALKER FONDAMENTI DI FISICA. FISICA MODERNA ZANICHELLI
P. G. BERGMANN INTRODUCTION TO THE THEORY OF RELATIVITY DOVER
L. LANDAU, E. LIFSHITZ FISICA TEORICA: TEORIA DEI CAMPI EDITORI RIUNITI
L. LANDAU, E. LIFSCHITZ FISICA TEORICA: MECCANICA QUANTISTICA EDITORI RIUNITI
J. J. SAKURAI MECCANICA QUANTISTICA MODERNA ZANICHELLI
P. A. M. DIRAC THE PRINCIPLES OF QUANTUM MECHANICS OXFORD UNIVERSITY PRESS
G. BUSIELLO, C. NOCE PROBLEMI DI FISICA TEORICA PATRON
L. ANGELINI MECCANICA QUANTISTICA: PROBLEMI SCELTI SPRINGER VERLAG
More Information
THE TEACHER CAN BE CONTACTED AT THE FOLLOWING EMAIL ADDRESSES: CNOCE@UNISA.IT OR CANIO@SA.INFN.IT
A MOODLE OF THE COURSE WILL ALSO BE ACTIVE AT THE FOLLOWING URL: HTTPS://AD.FISICA.UNISA.IT/LOGIN/INDEX.PHP
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