Pre-requisites (Vereiste voorkennis)
Chemische binding 1, 2 en 3 and moleculaire quantum mechanica;
Group theory is helpful but not required.
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Objectives (Leerdoelen)
The student is able to exploit rotational symmetry to solve atomic and molecular quantum mechanical problems.
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Contents (Beschrijving)
Symmetry can often be exploited to simplify or solve Atomic and Molecular quantum mechanical problems and ''group theory''; is the mathematical tool that is used. In quantum mechanics there is a connection between symmetries and observables. In this course we study rotational symmetry and the associated observable angular momentum. The mathematical groups related to this symmetry are known as SO(3) (rotation in three dimensions) and SU(2) (electron spin).
The following topics are treated:
- Rotations, infinitesimal rotations, SO(3), SU(2)
- Angular momentum operators and their commutation relations
- Spherical harmonics and rotations of molecules
- Rotation operators and their irreducible representations (Wigner D-matrices)
- Clebsch-Gordan coupling of angular momenta
- Spherical tensor operators
- The Wigner-Eckart theorem
- -3j, 6j, en 9j symbols
- density matrices and observables
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Literature (Literatuur)
- R. N. Zare, 'Angular Momentum', (1988, Wiley, New York)
- D. M. Brink and G. R. Stachler, 'Angular Momentum', (1962, Clarendon, Oxford)
- L. C. Biedenharn and J. D. Louck, 'Angular Momentum in Quantum Physics', (1981, Addison-Wesley, Reading)
- K. Blum, 'Density Matrix Theory and Applications', (1981, Plenum, New York)
- G. C. Groenenboom, 'Angular Momentum Theory and Applications', dictaat (pdf online)
- P. E. S. Wormer, 'Angular Momentum Theory', dictaat (pdf online)
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