FUNDAMENTALS OF QUANTUM MECHANICS: INTRODUCTION TO ELECTRICAL PROPERTIES OF THE MATTERIALS MOD. 2

The course is part of the core educational activities of Bachelor's Degree in Sustainable Chemistry and Technologies (Curriculum SCIENCES AND TECHNOLOGIES OF BIO AND NANOMATERIALS). Aim of this second part of the course is to investigate the chemical-physical properties of the materials that determine their electrical behavior when interacting with electric or magnetic fields or with electromagnetic radiation. The course will analyze the chemical-physical reasons that explain, for example, why metals conduct electricity and heat better than plastic, why some materials have a specific color, such as ruby, while others, like glass, are more or less transparent. The course deals with the study of these properties starting from the classical physical models and then passing to the use of the principles of quantum mechanics introduced in the first part of the course. The course highlights how these materials are used in the construction of many devices that we use every day and that the development of sustainable technologies derives from our ability to control their properties with extreme precision.

1) Knowledge and understanding:
i) Knowing and correctly defining the main electrical properties of materials and their classification based on their behavior.
ii) To know which physical phenomena determine their behavior
iii) To know how the phenomenological parameters are connected to the electronic properties of matter

2) Ability to apply knowledge and understanding
i) Knowing how to apply the most appropriate theoretical models for understanding and describing the electrical properties of materials
ii) Knowing which parameters can be used to modify these properties
iii) Know how the materials are selected for different applications

3) Judgment skills
i) Being able to evaluate the logical consistency of the models and the approximations used to describe the electrical properties of the materials.
ii) Knowing how to evaluate the intrinsic limits of the various models.

4) Communication Skills
i) Knowing how to describe the analyzed physical phenomena with an appropriate and scientifically correct language.
ii) Knowing how to justify the application of formalisms also from the mathematical point of view.
iii) Knowing how to interact with the teacher and the classmates by formulating coherent questions

5) Learning Ability
i) Knowing how to take notes also identifying eventual errors or inconsistencies during the lesson (sign errors, copying errors or not appropriately justified formalism changes)
ii) Knowing how to select information based on its relevance.
ii) Knowing how to connect knowledge independently within the course with knowledge deriving from other courses.

Having achieved the training objectives of the mathematics(I and II), general physics (I and II) and of course those related to the first part of the course. The student must know the main tools of differential and integral calculus and to solve simple differential equations. He must also know the basic concepts of quantum mechanics. This involves a certain familiarity in dealing with complex numbers and functions. In any case, a brief review of the main mathematical and physical topics will be performed before using a formalism.

In line with the training objectives and the expected learning outcomes, the contents of the course are divided as follows:
Introduction:
Description of course contents,
-The electron as a particle: the classical theory.
Conductivity and Ohm's law: Drude model
The Hall effect and measure of the density of charge carriers.
Electromagnetic wave in solids and plasma frequency.
- The electron as a wave: use of the quantum theory.
Review of the fundamental concepts and the Schrödinger equation: free electron, infinite potential hole, hydrogen atom.
The ionized hydrogen molecule: the Born-Oppenheimer approximation.
Free electrons in metals: the Sommerfield model of metals.
The density of states and the Fermi-Dirac distribution.
The periodic potential: band theory: Kronig-Penney model.
The effective mass and effective number of free electrons.
Number of states per band: Metal and isolator.
Intrinsic and extrinsic semiconductor.
p-n junction.
the diode: applications: rectifier
Dielectric materials and their applications.
Types of polarization:frequency response
Dielectric constant and refractive index.
The magnetic materials: Diamagnetism, parametricism and ferromagnetism.
Microscopic theory of magnetism
Hysteresis curves and magnetic domains.
Langevin function.
Classification of ferromagnetic materials based on the hysteresis curve and their technological uses.
Laser working principlesspontaneous emission and stimulated emission.

L.SOLYMAR,D. WALSH Lectures on the Electrical Properties of Materials. Oxford Science Pubblication.
JAMES D. LIVINGSTONElectronic Properties of Engineering Materials. Wiley
WEI GAO, NIGEL M. SAMMES An introduction to Electronic and Ionic Materials. World Scientific.
It is also suggested a popular scientifically rigorous text that can help to better understand the subject:
"Why Glass is Transparent" by B.S. Chandrasekhar. Publisher: Il Saggiatore unfortunately the Italian edition is out of print but you can find the original version
"Why Things Are the Way They Are" Cambridge University Press, 1998
Handouts provided by the lecturer

The assessment of learning takes place through an oral test during which the student must respond by demonstrating knowledge of the topics covered in the course. The student will be asked to illustrate, using the correct mathematical formalisms and the appropriate language, the most suitable physical models useful to describe the physical property discussed. He will have to demonstrate that he has understood both the formal aspect (use of the calculation techniques learned during the course) and the physical approximations inherent to each model.
The oral exam will last between 30-45 minutes and the evaluation will take into account the knowledge of the topics dealt with attention to the following aspects:
- Correct setting of the problem (definition of fundamental quantities, hypothesis and model adopted), the use of the mathematical formalism and knowledge of its physical interpretation.
-The exposure capacity (clarity, linearity and language properties)

The final grade will take into account the results achieved in both the tests of part 1 and 2

Teaching is organized in frontal lessons generally carried out on the blackboard. The course will include numerical exercises. The discussion is stimulated not only on the more technical aspects of the subject but also on the implications related to its interpretation.
In the "Moodle" platform of the University there are all the slides projected during the lessons.

Italian

STRUCTURE AND CONTENT OF THE COURSE COULD CHANGE AS A RESULT OF THE COVID-19 EPIDEMIC.

Accessibility, Disability and Inclusion

Accommodation and support services for students with disabilities and students with specific learning impairments:
Ca’ Foscari abides by Italian Law (Law 17/1999; Law 170/2010) regarding supportservices and accommodation available to students with disabilities. This includes students with mobility, visual, hearing and other disabilities (Law 17/1999), and specific learning impairments (Law 170/2010). In the case of disability or impairment that requires accommodations (i.e., alternate testing, readers, note takers or interpreters) please contact the Disability and Accessibility Offices in Student Services: disabilita@unive.it.

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