5 ECTS credits
135 h study time
Offer 1 with catalog number 1004236BNR for all students in the 1st semester at a (B) Bachelor - advanced level.
The course starts with a short introduction to quantum physics and with a short historical overview of all first attempts to describe systems consisting of small particles where the classical physical laws no longer apply.
- the time-dependent Schrödinger equation is derived. Some of the most important postulaten such as normalisation and the statistical interpretation are discussed.
- the time-independent Schrödinger is analysed and solved. Concepts such as stationary states and basis states are introduced.
- we solve the infinitely deep potential well.
- we introduce the formalism and postulates of quantum physics. Concepts such as hermitian operators and the uncertainty principle are discussed.
- we solve the quantum mechanical harmonic oscillator relying on creation and annihilation operators.
- the wave pack describing a free particle is introduced. We calculate for the sinc wave pack its propagation, expectation values of position and momentum and discuss the first order dispersion.
- we discuss the tunneling effect by solving Schrödinger’s equation with potential barrier.
- centro-symmetric are being discussed. As an example we give an overview of the hydrogen atom as illustration.
- we describe quantum mechanical systems with multiple particles. We discuss the differences between bosons and fermions.
- we give an introduction to quantum statistical physics and derive the occupation laws
- we study ideal gasses of quantum particles.
- the behaviour of particles in crystalline materials is described and applied to semiconductor materials
- Fermi’s golden rule.
None
This course has three goals
1. Developing knowledge about the physical mechanisms that determine the electrical, optical and magnetic properties of solid materials.
2. Provide mathematical tools to interpret and even predict quantitatively measurements results
3. Start from very basic physics and move on to very specific applications. This course will prepare the students to follow the lectures on Electronic components, Photonics, Materials, Laser Physics, Physics of optical materials and structures etc.
This course contributes to the following domain specific learning outcomes
The Bachelor of Engineering has a broad fundamental knowledge and understanding of
1. the scientific principles and methodology of the sciences, including the specificity of their applications in engineering;
2. fundamental basic methods and theories to schematise and to model problems or processes.
The Bachelor of Engineering can
1. reason in a logical, abstract and critical manner;
The Bachelor of Engineering has
1. a creative, problem-solving, results-oriented and evidence-backed posture aimed at innovation;
2. a critical attitude towards its own results and those of others;
3. means acquired for the collection of knowledge aimed at lifelong learning.
Subject-specific competences:
After studying this course the student should be able to answer the following questions and solve problems concerning the concepts mentioned
1. Determine the spectrum of the energy and the stationary states of a particle with mass m in an infinitely deep one-dimensional potential well of width L. Discuss if the spectrum is continuous or discrete? Is it divergent, convergent or equidistant? Is it degenerate or not? What is the ground state? Which is the probability density of the system in these energy states? Do you know realistic examples of such systems?
2. Starting from the results of the particle of mass m in a 1D infinitely deep potential well, determine the spectrum of energy and the stationary states of a particle of mass m in a 3D cubic box with rib L. Discuss the spectrum: is it continuous or discrete? Is it divergent, convergent or equidistant? Is it degenerate or not? What is the ground state? Which is the probability density of the system in these energy states? Do you know realistic examples of such systems? We have used these results elsewhere in the course? If so where?
3. Determine the spectrum of energy and the stationary states of a particle trapped in a finite 1D potential well of width L and height (or depth) V.
4. What is the tunnel effect? Calculate the transmission coefficient of a quantum particle with mass m colliding with a potential barrier of height V and width L. Discuss the tunnel regime and diffraction regime. Provide realistic conditions where the tunnel effect occurs and applications.
5. What is a wave pack? Study the quantum equivalent of the uniform directed motion of a quantum particle whose momentum is not known with infinite precision. Discuss the special case of the sinc wave pack. Show that there is a difference between the group velocity and the average phase velocity of the quantum particle.
6. What is the Schrödinger equation? Discuss the difference between the Schrödinger equation and a regular wave equation. Show that the Schrödinger equation is equivalent to a conservation law of probability. Where have we used the concept of probability current density in the course? What are stationary states in quantum physics?
7. Discuss the first five postulates of quantum mechanics. How do you describe in quantum physics the state of a system? And why? How do you describe the observable quantities and the results of the measurement?
8. What does the Heisenberg uncertainty principle state? Where have we found this principle in a natural way in the course?
9. What does the theorem of Ehrenfest say? Derive it starting from the Schrödinger equation.
10. What is a Boson? Give examples. What are the features of an ideal gas of Bosons? Derive the Bose Einstein distribution and discuss. What is Bose-Einstein condensation?
11. What is a Fermion? Give examples. Derive the Fermi-Dirac distribution and discuss. What are the features of an ideal Fermi gas at very low temperatures.
12. Calculate the Fermi energy of a 3D ideal Fermi gas at absolute zero temperature. What happens in 2D?
13. Discuss the model of Kronig Penney for the treatment of propagation of electric currents in ideal crystals. How can you infer on the basis of this model, the so-called Ek diagram? What are Brillouin zones? What happens if the crystal has a finite size?
14. Discuss the reduced Ek diagram of finite crystals in the model of Kronig and Penney. How do you make the distinction between conductors, semiconductors and dielectrics?
15. Discuss the concepts of crystal momentum and effective mass of charge carriers in a crystal. What are "holes"? Show orders of magnitude.
16. Determine for intrinsic semiconductors, the density of charge carriers as a function of the temperature and the effective masses. Calculate the Fermi level.
17. Explain what constitutes doping. Provide at least one example. Define and calculate in this case, the position of the donor level (or acceptor level). How does the Fermi energy evolve in case of n (p rep) doping?
18. Explain the main steps leading to Fermi’s golden rule. Discuss this. What are selection rules?
The final grade is composed based on the following categories:
Oral Exam determines 50% of the final mark.
Written Exam determines 50% of the final mark.
Within the Oral Exam category, the following assignments need to be completed:
Within the Written Exam category, the following assignments need to be completed:
The exam includes a written and an oral part. The written exam is open book and is quoted on half the points.
At the oral examination, students
- Give a detailed verbal discussion of a question from a questionnaire that is made available. This question is randomly chosen by the student.
- Give short and broad responses to two general knowledge 'culture questions "about the rest of the course material. here, understanding the physical mechanisms and knowledge of orders of magnitude of the effects are of interest
This offer is part of the following study plans:
Bachelor of Engineering: Electronics and Information Technology (only offered in Dutch)
Bachelor of Engineering: verkort traject elektronica en informatietechnologie na vooropleiding industriële wetenschappen (only offered in Dutch)