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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