Scattering of a particle on the $q$-deformed Euclidean space

• URL: http://arxiv.org/abs/2208.05723v1
• Date: Thu, 11 Aug 2022 09:40:00 GMT
• Title: Scattering of a particle on the $q$-deformed Euclidean space
• Authors: Hartmut Wachter
• Abstract summary: We develop a formalism for the scattering of a particle on the $q$-deformed Euclidean space. We write down $q$-versions of the Lippmann-Schwinger equation. We show that expressions for the wave functions of the scattered particle satisfy unitarity conditions.
• Score: 0.0
• License: http://creativecommons.org/licenses/by-nc-nd/4.0/
• Abstract: We develop a formalism for the scattering of a particle on the $q$-deformed Euclidean space. We write down $q$-versions of the Lippmann-Schwinger equation. Their iterative solutions for a weak scattering potential lead us to $q$-versions of the Born series. With the expressions for the wave functions of the scattered particle, we can write down S-matrix elements. We show that these S-matrix elements satisfy unitarity conditions. Considerations about the interaction picture for a quantum system in the $q$-deformed Euclidean space and a discussion of a $q$-version of time-dependent perturbation theory conclude our studies.

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