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Generalized Coherent States

Haeringen, T.M. van (2016) Generalized Coherent States. Bachelor's Thesis, Mathematics.

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In quantum physics coherent states are quantum states which have properties that closely resemble classical description. This thesis studies the notion of generalized coherent states, also called Gilmore-Perelomov coherent states. Firstly, we consider the coherent states associated to the harmonic oscillator. These can be described as the set of states resulting from a representation of the Weyl-Heisenberg group acting on the ground state of the harmonic oscillator. Gilmore-Perelomov coherent states generalize this idea; for an arbitrary Lie group we can define generalized coherent states as the states resulting from the action of an irreducible, unitary representation of a Lie group on some fixed state. If the fixed state is chosen to have minimal uncertainty, we obtain a set of coherent states that have minimal uncertainty and are closest to classical in this sense. As examples we examine the coherent states resulting from representations of the Lie groups SU(2) and SU(1, 1).

Item Type: Thesis (Bachelor's Thesis)
Degree programme: Mathematics
Thesis type: Bachelor's Thesis
Language: English
Date Deposited: 15 Feb 2018 08:14
Last Modified: 15 Feb 2018 08:14

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