Learning outcomes

This course presents the basic principles of quantum mechanics, and study specific applications, with particular emphasis on topics of interest to students in electrical and computer engineering. The course develops the quantum mechanical foundation for modern electronic devices and quantum technology, for example MEMS, lasers, transistors, LEDs, quantum size effects in FETs, optical communication, semiconductor nanostructures, etc.

At the end of this course the student will be able to:

By the completion of the lectures, the students should have been introduced to the following and be able to:

1. Solve time-independent Schrödinger’s Equation in simple potentials

2. Fully analyze the behavior of a quantum harmonic oscillator and apply it in several problems

3. Understand the time-dependent Schrödinger Equation and the superposition principle

4. Understand quantum operators and compute expectation values for physical quantities

5. Calculate the transmission coefficient in various tunneling problems, including resonant tunneling in semiconductor nanostructures

6. Understand the Dirac formalism of quantum mechanics and perform calculations using bra-ket notation 

7. Obtain approximate solutions of the time-independent Schrödinger Equation using first and second-order perturbation theory

8. Understand and be able to apply degenerate perturbation theory

9. Understand the Kronig-Penney model and the tight binding model and apply it in solids and in particular semiconductors

10. Understand time-dependent perturbation theory and Fermi’s Golden Rule and apply it in specific problems

11. Work with angular momentum operators and spherical harmonics

12. Solve Schrödinger’s Equation for the hydrogen atom and other three-dimensional problems appropriate for semiconductor nanostructures 

13. Understand spin and the structure of qubits

14. Understand lasers

16. Understand basic quantum technology applications

The course belongs to Levels 6 of the European Qualifications Framework for Lifelong Learning.

General Competences

Search for, analysis and synthesis of data and information, with the use of the necessary technology

Adapting to new situations

Working independently

Team work

Working in an interdisciplinary environment

Production of new research ideas

Production of free, creative and inductive thinking

Basic features: time-dependent and time-independent Schrödinger equation, wavefunction, operators, expectation values, uncertainty principal.

Quantum mechanics in basic systems: bound states in simple and complex one-dimensional potential wells and applications in semiconductor nanostructures and heterostructures.

Scattering in one dimensional quantum structures. The propagation matrix. Applications in semiconductor nanostructures.

Periodic potentials and applications in solids with emphasis in semiconductors. Tight binding method and application in a simple one-dimensional lattice.

Axioms of quantum mechanics, Dirac formalism and matrix formulation.

The harmonic oscillator: standard solution and description with creation and annihilation operators; applications in quantum nanostructures and electromagnetic fields and their quantization, photons. Quantization of the LC circuit. Free electron in a magnetic field - Landau states and connection to the semiclassical orbit.

Quantum confinement in three-dimensions: separable potentials, central potentials, and applications in three-dimensional semiconductor nanostructures (“hard” spherical potential and finite spherical potential) and the hydrogen-like systems and applications in defects in semiconductors and excitons in semiconductors.

Angular momentum and spin.

Semiconductor quantum wells, wires and dots.

Time-independent perturbation theory and its applications. Examples, Stark effect in quantum wells and the displayed harmonic oscillator. Time-independent degenerate perturbation theory and applications, the sudden approximation, and applications.

Time-dependent perturbation theory, two-level quantum system and interaction of light with quantum systems, spontaneous and induced transitions, Einstein coefficients, Fermi's Golden Rule, incoherent and coherent dynamics in a two-level system, applications in lasers and quantum technology at the nanoscale.

Characteristics of High frequency and RF receivers, design parameters of transceivers, Noise Figure, non-linearities, Dynamic Range.

Phase –locked –loops (PLL) and their design parameters. PLL stability, analog and digital Phase detectors, voltage –controlled oscillators (VCO). Applications of PLL in telecommunications (frequency synthesizers, demodulators, carrier and timing recovery subsystems). 

Analysis and design of high frequency (RF, IF) receiver amplifiers with emphasis on low noise performance (Low –noise amplifiers- LNA).

RF power amplifiers for the transmitter. Matching for high transmitted power.

Analysis and design of mixer circuits and analog multiplier circuits.

Circuits for implementation of FM and PM modulators and demodulators.

Examples of RF receiver systems for wireless applications.

DELIVERY

Face-to-face

USE OF INFORMATION AND COMMUNICATIONS TECHNOLOGY

The teaching of the course is done mainly using a blackboard where the theory is thoroughly analyzed. Also, a computer and a related projection equipment is used where computer demonstration laboratories are held where either freely available computer programs or computer programs written by the lecturer are used to solve of the relevant equations and the visualization of the results in figures. These programs will be explained to students and made available to students for their use. Using eclass to interact with students and support teaching.

TEACHING METHODS

STUDENT PERFORMANCE EVALUATION

Students will be evaluated using a combination of the following. Exercises/problems during the year and their delivery at regular intervals (40 %) and a final written exam with exercises and critical questions/problems (60 %). Alternatively, only a final exam with exercises and critical questions/problems may be chosen.

·         D. K. Ferry, Quantum Mechanics: An Introduction for Device Physicists and Electrical Engineers, 3^rd edition, CRC Press, 2021

·         C. L. Tang, Fundamentals of Quantum Mechanics for Solid State Electronics and Optics, Cambridge, 2005

·         A. F. J. Levi, Applied Quantum Mechanics, 2^nd edition, Cambridge, 2006

·         A. Yariv, Quantum Electronics, 3^rd edition, Wiley, 1991

·         J. Singh, Quantum Mechanics: Fundamentals & Applications to Technology, Wiley, 1997

·         D. M. Kim, Introductory Quantum Mechanics for Applied Nanotechnology, Wiley, 2015

·         D. G. Steel, Introduction to Quantum Nanotechnology, Oxford, 2021

·         V. V. Mitin, D. I. Sementsov, and N. Z. Vagidov, Quantum Mechanics for Nanostructures, Wiley, 2006