2006/03/26 by C. B. Compean, Compean, C. B., M. Kirchbach +1
Mathematics · Physics and Astronomy · #Algebraic and Geometric Analysis #Quantum Mechanics and Non-Hermitian Physics #Quantum chaos and dynamical systems #quant-ph
paper · pdf · doi:10.48550/arxiv.quant-ph/0603232
10 pages, 6 figures
arxiv created 2006/03/26 · arxiv updated 2009/12/01
We present the quantum mechanics problem of the one-dimensional Schroedinger equation with the trigonometric Rosen-Morse potential. This potential is of possible interest to quark physics in so far as it captures the essentials of the QCD quark-gluon dynamics and (i) interpolates between a Coulomb-like potential (associated with one-gluon exchange) and the infinite wall potential (associated with asymptotic freedom), (ii) reproduces in the intermediary region the linear confinement potential (associated with multi-gluon self-interactions) as established by lattice QCD calculations of hadron properties. Moreover, its exact real solutions given here display a new class of real orthogonal polynomials and thereby interesting mathematical entities in their own.