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arXiv · 2208.05723

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

Hartmut Wachter
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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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Hartmut Wachter. 2022-08-11. Scattering of a particle on the $q$-deformed Euclidean space. https://arxiv.org/abs/2208.05723

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