I. Concepts and tools for single particle systems
1. Why quantum physics?
The impact of quantum physics on our understanding of the world around us and all its applications, especially in ICT.
2. How to do quantum physics?
A first answer to the three basic questions implicit to any paradigm in theoretical physics (description of the state of the systems, its evolution and its properties).
3. The mathematical formalism
Linear algebra with a important focus on Hilbert spaces, Hermitian operators, commutators, eigenvalues and -vector, spectral properties.
4. The six axioms of NRQP
The fundamental assumptions one has to accept to build and use the NRQF framework.
5. The operational tools of NRQP
Averages and uncertainties, Heisenberg relations, operators relating to measurable quantities and the Schrodinger equation as a conservation law.
II. Illustrations of single particle systems
6. Particle in a closed box (1D, 2D, 3D)
7. Particle in a finite potential well
Next to the introduction of systems with bound and unbound states, an exploration of the analogy with guided waves.
8. Particles and barriers, tunneling
9. The wave packet
A step beyond the particle as a point and the introduction of concepts such as particle, phase and group velocity.
10. Particle on a spring
The quantum harmonic oscillator and its importance in quantum optics.
III. Concepts and tools of equilibrium statistical NRQP
11. The problem with many particle systems
Why the naive approach does not work.
12. Bosons and Fermions
Different assumptions lead to a different behaviour of particle that pop-up in the quantum realm and which relate to their thermodynamical distributions.
13. Band theory of crystals
The Kronig-Penney model, reading energy-wavevector diagrams, generalization for real crystals, crystal momentum and effective mass approximations, electronic and photonic bandgaps.
14. Charge transport in semiconductors
Intrinsic and extrinsic semiconductors, doping with donors and acceptors, the relation with gasses and their Fermi level, band-bending in diode junctions
IV. Introduction to spectroscopy
15. Fermi's Golden Rule
First order perturbation analysis, both time-independent and time-dependent, the selection rules that follow and the application to real-world problems.
This course 's objectives are :
1.To give the students the necessary insights and skills required to understand the physics behind the electronic and optoelectronic properties of solid state materials in general and of semiconductor structures in particular.
2.To prepare the students for courses concerning electronic components, lasers, optical materials, (opto-)electronic systems, non-linear and quantum optics etc.
This course contributes to the following domain specific learning outcomes:
1. Master and apply advanced knowledge in the own field of engineering in case of complex problems.
2. Understand and apply the properties of the most important optical materials.
3. Analyse complex problems and convert them into scientific questions.
4. Select and apply the proper models, methods and techniques.
5. Develop and validate mathematical models and methods.
6. Report on technical or scientific subjects orally, in writing and in graphics
7. Interpret the historical evolution of the own field of engineering and its social relevance.
8. Dispose of enough knowledge and comprehension to control the results of complex calculations or make approximate estimates.
Specific course competences:
At the end of the course the students should be able to address all the following questions and solve problems related to these matters.
1. Explain the five first basic postulates of quantum physics, explain their background and briefly give examples from the course that illustrate their importance.
2. Why do you need a Hilbert space and Hermitic Operators in quantum physics? Give examples of Hermitic operators and non Hermitic Operations.
3. What is time dependent Schrödinger’s equation? Discuss the difference between Schödinger’s equation and a wave equation. Show that Schödinger’s equation is equivalent with a conservation law for the density of probability to find a particle in a specific position.
4. What is a stationary state in quantum physics for a single particle and in a N-body system? Discuss and give examples
5. How do you define the expectation value and uncertainty of a physical quantity in a specific state in non relativistic quantum physics?
6. Determine the energy spectrum and stationary states of one particle with mass m in an one dimensional infinite potential well. Discuss. Do you know realistic examples of such systems?
7. Determine the energy spectrum and stationary states of one particle with mass m in a three dimensional infinite potential well. You can start from the results obtained in question 6. What is a density of states?
8. What is the tunneling? Determine the transmission coefficient for a particle with mass m coming from minus infinity with energy E and encountering a 1D potential barrier of height V and width a. Discuss the tunnel and diffraction regime. Give examples of applications of tunneling.
9. What is a wave packet? Discuss the quantum equivalent of the propagation of a free particle whose momentum is not known with infinite precision. Give the example of a Gaussian wave packet. What is the difference between phase velocity and group velocity?
10. Derive the energy spectrum and stationary states of a 1D harmonic oscillator with mass m and classical pulsation w. Use the technique of creation and destruction operators.
11. Discuss Heisenberg’s uncertainty principle. Relate it to the commutator properties of operators. Give examples in the course where Heisenberg’s principle plays a crucial role.
12. What is a Boson? Give examples. What are the properties of an ideal boson gas? Derive the Bose - Einstein distribution and discuss.
13. What is a Fermion? Give examples. What are the properties of an ideal Fermi gas? Derive Fermi –Dirac’s distribution and discuss.
14. Derive the Fermi-energy of a 3D ideal Fermi gas at absolute zero temperature. What happens in 2D?
15. Discuss ( without doing the maths completely) the Kronig Penney model for the propagation of electrons in infinite crystals. What is a reduced E-k diagram? What happens when the crystal has finite length? What is the difference between a conductor, a semi conductor and an isolator?
16. Discuss the concepts crystal momentum and effective mass of charge carriers in crystals. What are holes? Give orders of magnitute of the effective masses of electrons and holes in Si and GaAS.
17. What are the typical densities of charge carriers in intrinsic semiconductors, as a function of temperature and effective mass? Calculate the position of their Fermi level.
18. Discuss doping of semiconductors. Give at least one example. Define and calculate the position of a donor and /or an acceptor level. How does the Fermi level change as a function of doping ?
19. Give the essential steps leading to Fermi Golden rule What are selection rules?