Integrability of the one dimensional Schrödinger equation

Abstract : We present a definition of integrability for the one-dimensional Schrödinger 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 of boundary conditions. We then make a complete classification of rational integrable potentials. Many new integrable cases are found, some of them physically interesting.
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Contributor : Imb - Université de Bourgogne <>
Submitted on : Monday, March 5, 2018 - 3:12:23 PM
Last modification on : Friday, June 8, 2018 - 2:50:07 PM

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Thierry Combot. Integrability of the one dimensional Schrödinger equation. Journal of Mathematical Physics, American Institute of Physics (AIP), 2018, 59 (2), ⟨10.1063/1.5023242⟩. ⟨hal-01723458⟩



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