Clebsch-Gordan Coefficients

Clebsch-Gordan Coefficients: A Quantum Mechanical and Mathematical Perspective

de Vries, Olaf (TU Delft Applied Sciences; TU Delft Electrical Engineering, Mathematics and Computer Science)

de Laat, D. (mentor)
Nazarov, Y.V. (mentor)
Groenevelt, W.G.M. (graduation committee)
Otte, A.F. (graduation committee)

Delft University of Technology

2021-06-30

In this work, Clebsch-Gordan coefficients are studied from both a quantum mechanical and a mathematical perspective. In quantum mechanics, Clebsch-Gordan coefficients arise when two quantum systems with a certain angular momentum are combined and the total angular momentum is to be found. We start by discussing the relevant postulates of quantum mechanics. From there we move on to a discussion of quantum angular momentum, the combining of quantum systems, and Clebsch-Gordan coefficients. Finally, an algorithm for calculating the Clebsch-Gordan coefficients is developed. A firm grasp of linear algebra is required to understand this quantum mechanical perspective. The mathematical perspective is rooted in representation theory. The Clebsch-Gordan coefficients show the decomposition of the tensor product of irreducible representations of the three dimensional rotation group into the direct sum of irreducible representations. We explain the necessary theory to understand how this works. This includes a discussion of irreducible unitary representations, spherical harmonics, direct sum representations, and tensor product representations. Some experience with group theory is required to understand the mathematical perspective.

Clebsch-Gordan Coefficients
Quantum
Representation Theory
Angular Momentum
Quantum Angular Momentum
Ladder Operator
Quantum Mechanics
Optimization

http://resolver.tudelft.nl/uuid:8eb650e8-b255-4e12-bc0b-a9ada84092e4

Student theses

bachelor thesis

© 2021 Olaf de Vries