2022/08/11 by Hartmut Wächter, Wachter, Hartmut
Mathematics · Physics and Astronomy · #16T05 (Secondary) #81R50 (Primary) #Algebraic structures and combinatorial models #FOS: Physical sciences #Nonlinear Waves and Solitons #Quantum Mechanics and Non-Hermitian Physics #Quantum Physics (quant-ph)
paper · pdf · doi:10.48550/arxiv.2208.05723
openalex publication_date 2022/08/11 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.