2011/12/20 by Veronika Gáliková, Gáliková, Veronika, P. Prešnajder +2 · 1 citation
Mathematics · Physics and Astronomy · #FOS: Physical sciences #High Energy Physics - Theory (hep-th) #Mathematical Physics (math-ph) #Noncommutative and Quantum Gravity Theories #Quantum Mechanics and Applications #Quantum Mechanics and Non-Hermitian Physics #hep-th #math-ph #math.MP
paper · pdf · doi:10.48550/arxiv.1112.4643
18 pages
arxiv created 2011/12/20 · openalex publication_date 2011/12/20 · arxiv updated 2011/12/21 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We investigate consequences of space non-commutativity in quantum mechanics of the hydrogen atom. We introduce rotationally invariant noncommutative space \bf R30 - an analog of the hydrogen atom (H-atom) configuration space \bf R30 = \bf R3∖ \0\. The space \bf R30 is generated by noncommutative coordinates realized as operators in an auxiliary (Fock) space \cal F. We introduce the Hilbert space \calH of wave functions ψ formed by properly weighted Hilbert-Schmidt operators in \cal F. Finally, we define an analog of the H-atom Hamiltonian in \bf R30 and explicitly determine the bound state energies Eλn and the corresponding eigenstates ψλnjm. The Coulomb scattering problem in \bf R30 is under study.