2016/09/14 by Thierry Combot, Combot, Thierry
Mathematics · Physics and Astronomy · #34M46 #34M50 #37J30 #FOS: Physical sciences #Mathematical Physics (math-ph) #Nonlinear Waves and Solitons #Numerical methods for differential equations #Quantum chaos and dynamical systems #math-ph #math.MP #msc:34M46 #msc:34M50 #msc:37J30
paper · pdf · doi:10.48550/arxiv.1609.04348
56 pages, 2 figures
arxiv created 2016/09/14 · openalex publication_date 2016/09/14 · arxiv updated 2016/09/15 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We present a definition of integrability for the one dimensional Schroedinger equation, which encompasses all known integrable systems, i.e. systems for which the spectrum can be explicitly computed. For this, we introduce the class of rigid functions, built as Liouvillian functions, but containing all solutions of rigid differential operators in the sense of Katz, and a notion of natural boundary conditions. We then make a complete classification of rational integrable potentials. Many new integrable cases are found, some of them physically interesting.