# Atomic Physics

## Learning outcomes of the course unit

To know and understand 1) the phenomena which brought to the classical electromagnetism crisis, 2) the simplest formalisms of quantum-mechanics, 3) their application to systems of relevance to electronic and telecommunication engineering, 4) the electrons behaviour in solids, and 5) the derived technological applications.

Being able to relate the topics learned, not only one to each other, but also to those of the basic and related disciplines.

Being able 1) to apply the knowledge and understanding of the above issues related to simple, but basic systems, to the study of electronic devices, 2) to extend them to more complex systems which will be encountered by the engineer in view of new technological developments, and 3) to understand and use properly and profitably the results offered by the experimental techniques for material characterization.

Being able to update the acquired skills by consulting the scientific papers published in the specific area.

Applying knowledge and understanding of 1) the phenomena which brought to the classical electromagnetism crisis, 2) the simplest formalisms of quantum-mechanics, 3) their application to systems of relevance to electronic and telecommunication engineering, 4) the electrons behaviour in solids, and 5) the derived technological applications.

Ability to apply the knowledge and understanding of the above issues related to simple, but basic systems 1) to the study of electronic devices, 2) to extend them to more complex systems which will be encountered by the engineer in view of new technological developments, and 3) to understand and use properly and profitably the results offered by the experimental techniques for material characterization.

## Prerequisites

Mathematics. General Physics.

Mathematics. General Physics.

## Course contents summary

Introduction to modern physics topics and their applications, including a) the experiments which brought to the quanta theory, b) the quantum-and wave-mechanical approach. The quantum-mechanics is applied to simple systems, but of relevance to understand the microscopic mechanisms which 1) determine the properties of materials and 2) originate the experimental investigation techniques of specific interest for electronic and telecommunication engineering.

Introduction to modern physics topics and their applications, including a) the experiments which brought to the quanta theory, b) the quantum-and wave-mechanical approach. The quantum-mechanics is applied to simple systems, but of relevance to understand the microscopic mechanisms which 1) determine the properties of materials and 2) originate the experimental investigation techniques of specific interest for electronic and telecommunication engineering.

## Course contents

A. Experiments which brought to the quanta theory (about 16 hours), with reference to the following topics.

Gas discharge. Mass spectrometry. Compton and photoelectric effects. Atomic and X-ray spectra. Stern-Gerlach experiment. X-ray and particle diffraction experiments. Electron microscope (SEM and TEM). Blackbody emission.

B. Quantum Mechanical approach to simple systems (about 26 hours), with reference to the following topics.

Uncertainty, correspondence, and complementarity principles. Vibrating string equation. Eigenfunctions and eigenvalues. Quantum mechanics postulates.

Free particle in a box: Schrödinger equation. Energy levels. Probability density. Application to free electrons in metals, quantum wells, colour centres.

Harmonic oscillator: Schrödinger equation. Energy levels. Probability density. Application to vibrational spectra of heteronuclear molecules and lattice vibrations in solids. Anharmonicity.

Hydrogen and hydrogenoid atoms: Schrödinger equation. Energy levels. Probability density. Rigid rotor, as simplified case. Application to rotational spectra of heteronuclear molecules.

Potential wall and tunnel effect. Tunnel junctions. Tunnel microscope (STM).

Energy bands in crystalline solids. Kronig-Penney model. Classification of solids according to band theory. Electron dynamics. Effective mass. Fermi-Dirac statistics. Electrical conductivity. Photonic crystals. Optical properties of semiconductors and insulators.

A. Experiments which brought to the quanta theory (about 16 hours)

Gas discharge. Compton and photoelectric effects. Atomic and X-ray spectra. Stern-Gerlach experiment. X-ray and particle diffraction experiments. Electron microscope (SEM and TEM). Blackbody emission.

B. Quantum Mechanical approach to simple systems (about 26 hours)

Uncertainty, correspondence, and complementarity principles. Vibrating string equation. Eigenfunctions and eigenvalues. Quantum mechanics postulates.

Free particle in a box: Schrödinger equation. Energy levels. Probability density. Application to free electrons in metals, quantum wells, colour centres.

Harmonic oscillator: Schrödinger equation. Energy levels. Probability density. Application to vibrational spectra of heteronuclear molecules and lattice vibrations in solids. Anharmonicity.

Hydrogen and hydrogenoid atoms: Schrödinger equation. Energy levels. Probability density. Rigid rotor, as simplified case. Application to rotational spectra of heteronuclear molecules.

Potential wall and tunnel effect. Tunnel junctions. Tunnel microscope (STM).

Energy bands in crystalline solids. Kronig-Penney model. Classification of solids according to band theory. Electron dynamics. Effective mass. Fermi-Dirac statistics. Electrical conductivity. Photonic crystals. Optical properties of semiconductors and insulators.

## Recommended readings

Eisberg R., Resnick R. Quantum Physics of Atoms, Molecules, Solids and Nuclei, John Wiley ed. (New York), 1985.

Halliday D., Resnick R., Walker J. Fondamenti di Fisica: Fisica Moderna, V edizione, Casa Editrice Ambrosiana, Milano (in italian), 2002.

Capelletti R., Fisica Atomica, Notes of the course (in italian), 2017.

Eisberg R., Resnick R. Quantum Physics of Atoms, Molecules, Solids and Nuclei, John Wiley ed. (New York), 1985.

Halliday D., Resnick R., Walker J. Fondamenti di Fisica: Fisica Moderna, V edizione, Casa Editrice Ambrosiana, Milano (in italian), 2002

Capelletti R., Fisica Atomica, Notes of the course (in italian), 2016.

## Teaching methods

Lectures integrated by a limited number (2-3 hours) of exercises presented by the teacher to clarify some mathematical issues.

The teacher is available for further explanations on demand of the student by means of e-mail or phone call.

Lectures integrated by a limited number (2-3 hours) of exercises presented by the teacher to clarify some mathematical issues.

## Assessment methods and criteria

The test is verbal.

The student is required to expose in concise, but comprehensive way, the program subject proposed by every question. The presentation should prove that the student has assimilated the related basic concepts and is able to present them in autonomous, clear, and correct manner. The recitation of the argument learned by heart in uncritical way is not admitted. As a rule two subjects are proposed to the student, each of them related to one of the two main topics of the program (A and B items of the extended program, respectively).

The test is verbal.

The student is required to expose in concise, but comprehensive way, the program subject proposed by every question. The presentation should prove that the student has assimilated the related basic concepts and is able to present them in autonomous, clear, and correct manner. The recitation of the argument learned by heart in uncritical way is not admitted. As a rule two subjects are proposed to the student, each of them related to one of the two main topics of the program (A and B items of the extended program, respectively).

## Other informations

The Power Point presentation of the lectures of the whole course will be available to students (on demand to the teacher) at the beginning of the course.

The Power Point presentation of the lectures of the whole course will be available to students (on demand to the teacher) at the beginning of the course.