2023/04/12 by Guillermo Gordillo-Núñez, Gordillo-Núñez, Guillermo, R. Álvarez-Nodarse +3
Physics and Astronomy · #Cold Atom Physics and Bose-Einstein Condensates #Exactly Solvable and Integrable Systems (nlin.SI) #FOS: Physical sciences #Mathematical Physics (math-ph) #Nonlinear Photonic Systems #Quantum Mechanics and Non-Hermitian Physics #Quantum Physics (quant-ph)
paper · pdf · doi:10.48550/arxiv.2304.06730
openalex publication_date 2023/04/12 · openalex created_date 2023/04/19 · openalex updated_date 2026/08/01
We rigorously solve the time-independent Schrödinger equation for the Rosen-Morse type potential. By using the Nikiforov-Uvarov method, we obtain, in a systematic way, the complete solution of such equation, which includes the so-called bound states (square-integrable solutions) associated with the discrete spectrum, as well as unbound states region (bounded but not necessarily square-integrable solutions) related to the continuous part of the spectrum. The resolution of this problem is used to show that the kinks of the non-linear Klein-Gordon equation with φ2p+2 type potentials are stable. We also derive the orthogonality and completeness relations satisfied by the set of eigenfunctions which are useful in the description of the dynamics of kinks under perturbations or interacting with antikinks.