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- The student knows the special aspects of quantum systems comprising of identical particles
- The student is able to perform calculations in the Fock-space of particles or quasi-particles
- The student can deal with quantum mechanical ensembles
- The student has the ability to perform teamwork and explain an advanced topic to fellow students
- The student understands the quantization aspects of electromagnetic fields (module 1)
- The student knows the fundamental aspects of relativistic quantum mechanics (module 1)
- The student understands the basic concepts and methods of condensed matter theory (module 2)
- The student understands such phenomena as Josephson effect, Andreev reflection, Aharonov-Bohm effect, conductance quantization, magnetoresistance and Hall effect and can apply theory methods to describe them (module 2)
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This course is part of a chain of quantum mechanics courses, consisting of Introduction to Quantum Mechanics and Quantum Mechanics 1a+b, 2 and 3.
During the 3rd quarter the emphasis in Quantum Mechanics 3 is on the properties of identical-particle systems. By adopting the occupation number representation, the quantum space of identical-particle systems (Fock-space) is constructed in terms of creation and annihilation operators. In this context the student will encounter new concepts such as quasi-particles and second quantization. Next the quantum-mechanical concept of mixed ensembles is introduced, which is subsequently used to derive the quantum statistics of non-interacting many-particle systems that are in thermodynamic equilibrium with a macroscopic environment. In the 4th quarter the course splits into two modules. The students are free to choose either of these modules.
Module 1 (W.J.P. Beenakker) is meant for students who are interested in the master's specialisation "Particle and Astrophysics". In this module it will be shown how the problems with the construction of a 1-particle version of relativistic quantum mechanics can be circumvented by assigning a many-particle interpretation to the relativistic wave equations. The latter is illustrated and motivated by the quantization of the electromagnetic field.
Module 2 (M. Titov) is meant for students who are interested in the master's specialisation "Physics of Molecules and Materials". This module covers the basic concepts of condensed matter theory: Bloch theorem, tight-binding models, k-dot-p Hamiltonians, spin-orbit interaction, dispersion relations, density of states, current operator, and scattering states. The following topics will be treated: the Landauer-Büttiker theory of quantum transport, the Boltzmann kinetic equation, the mean-field method and the Ginzburg-Landau theory of superconductivity.
The students are expected to participate in one team assignment. As part of a team of 3-4 students they should prepare and present a mini-lecture on a modern/advanced quantum mechanical topic. These presentation assignments are integrated in the exercise-classes and are meant to provide added depth to a particular discussion or to introduce the students to a ground-breaking experiment that is described in Nature or Physical Review Letters.
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• Written Exam • A Bonus may be obtained by handing in exercise class assignments. |
| | Required materialsReaderLecture notes: will be updated on a weekly basis and can be downloaded before each lecture |
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| Recommended materialsBookDavid J. Griffiths, Introduction to Quantum Mechanics, 2nd edition, Prentice Hall, Pearson Education Ltd, 2005 |
| BookEugene Merzbacher, Quantum Mechanics, 3rd edition, John Wiley & Sons, 2003 |
| BookB.H. Bransden and C.J. Joachain, Quantum Mechanics, 2nd edition, Prentice Hall, Pearson Education Ltd, 2000 |
| BookF. Schwabl, Advanced Quantum Mechanics, 3rd edition, Springer 2005 |
| BookD. Feng and G. Jin, Introduction to condensed matter physics, World Scientific, Singapore 2005 |
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| Instructional modesLecture
| Tutorial
| Zelfstudie
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| TestsExamTest weight | | 1 |
Test type | | Written exam |
Opportunities | | Block KW4, Block KW4 |
RemarkThere will be a single exam that covers both modules
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