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Vermeulen, Joop (author)In this thesis, we will be studying Lie groups and their connection to certain orthogonal polynomials. We will look into the classical Krawtchouk, Meixner and Laguerre polynomials, and the multivariate Krawtchouk and Meixner polynomials as defined by Iliev. Using representations of the Lie groups SU(2) and SU(1,1), it will be shown that the...master thesis 2022
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Rozenbroek, Dani (author)De Wilson en Racahpolynomen zijn hypergeometrische orthogonale polynomen die helemaal bovenaan staan in het Askeyschema. Deze polynomen zijn de meest algemene hypergeometrische orthogonale polynomen in één variabele en generaliseren de andere hypergeometrische orthogonale polynomen in het Askeyschema.<br/><br/>In deze scriptie wordt ingegaan...bachelor thesis 2022
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van Gulik, Quirijn (author)Representation theory is a branch in mathematics that studies group homomorphisms between a group and the automorphism group of a vector space. A special representation that every group has is the regular representation. This representation permutes all elements of the group in a vector space which dimension is equal to the order of the group....bachelor thesis 2021
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Farrokhi, Shayan (author)In this thesis we provide an elementary introduction in finite dimensional representation theory of the Lie groups SU(2) and SU(3) for undergraduate students in physics and mathematics. We will also give two application of representation theory of these two groups in physics: the spin and quark models. We begin with first discussing...bachelor thesis 2021
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de Vries, Olaf (author)In this work, ClebschGordan coefficients are studied from both a quantum mechanical and a mathematical perspective. In quantum mechanics, ClebschGordan 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...bachelor thesis 2021
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Camps, Sean (author)In this paper we will naturally extend the concept of Fourier analysis to functions on arbitrary groups. We will generalise the idea of a convolution and try to find a formula for Fourier coefficients in such way that the coefficients of the convolution can easily be calculated. In the first section we will start off in familiar territory as we...bachelor thesis 2021
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Niestijl, Milan (author)Recent progress on the representation theory of certain infinite dimensional gauge groups has raised an interest in the strongly continuous unitary representations of groups of a specific form that satisfy a certain positive energy condition. An equivalent formulation of the positive energy condition is obtained, allowing for a geometrical...master thesis 2019
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Mol, Jan (author)The Racah polynomial Rn(λ(x)) is a polynomial of degree n and is variable in λ(x). In this thesis two properties of this polynomial will be studied. One is the orthogonal property of the Racah polynomial. And the other is that the Racah polynomial can also be described as a polynomial of degree x and variable over λ(n). The Racah polynomials...bachelor thesis 2019
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Quantum information in the real world: Diagnosing and correcting errors in practical quantum devicesHelsen, J. (author)Quantum computers promise to be a revolutionary new technology. However, in order to realise this promise many hurdles must first be overcome. In this thesis we investigate two such hurdles: the presence of noise in quantum computers and limitations on the connectivity and control in large scale quantum computing architectures.In order to combat...doctoral thesis 2019
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van der Toorn, R. (author)We revisit RossbyHaurwitz planetary wave modes of a twodimensional fluid along the surface of a rotating planet, as elements of irreducible representations of the so(3) Lie algebra. Key questions addressed are, firstly, why it is that the nonlinear selfinteraction of any RossbyHaurwitz wave mode is zero, and secondly,<br/>why the phase...journal article 2019
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Slob, E.C. (author), Wapenaar, C.P.A. (author)It is shown that the electromagnetic Green's functions of any linear medium with arbitrary heterogeneity can be obtained from the cross?correlation, or the cross?convolution, of two recordings at different receiver locations in an open system. Existing representations are known for cross?correlations where time?reversal invariance is exploited...journal article 2007