1994/04/06 by Wolfgang Weich, Weich, Wolfgang · 1 citation
Mathematics · Physics and Astronomy · #Algebraic structures and combinatorial models #FOS: Physical sciences #High Energy Physics - Theory (hep-th) #Quantum Mechanics and Non-Hermitian Physics #Quantum chaos and dynamical systems #Spectral Theory in Mathematical Physics #hep-th
paper · pdf · doi:10.48550/arxiv.hep-th/9404029
24 pages, report LMU-TPW 1994-5
arxiv created 1994/04/06 · openalex publication_date 1994/04/06 · arxiv updated 2016/09/06 · openalex created_date 2025/10/24 · openalex updated_date 2026/07/28
The observable algebra O of SOq(3)-symmetric quantum mechanics is generated by the coordinates of momentum and position spaces (which are both isomorphic to the SOq(3)-covariant real quantum space Rq3). Their interrelations are determined with the quantum group covariant differential calculus. For a quantum mechanical representation of O on a Hilbert space essential self- adjointness of specified observables and compatibility of the covariance of the observable algebra with the action of the unitary continuous corepresent- ation operator of the compact quantum matrix group SOq(3) are required. It is shown that each such quantum mechanical representation extends uniquely to a self-adjoint representation of O. All these self-adjoint representations are constructed. As an example an SOq(3)-invariant Coulomb potential is intro- duced, the corresponding Hamiltonian proved to be essentially self-adjoint and its negative eigenvalues calculated with the help of a q-deformed Lenz-vector.