2011/04/18 by Jose Franco, Jose A. Franco, Franco, Jose +1
Mathematics · Physics and Astronomy · #22E70 #35Q41 #Advanced Algebra and Geometry #Advanced Topics in Algebra #FOS: Mathematics #FOS: Physical sciences #Homotopy and Cohomology in Algebraic Topology #Mathematical Physics (math-ph) #Mathematical and Theoretical Analysis #Nonlinear Waves and Solitons #Quantum Mechanics and Non-Hermitian Physics #Representation Theory (math.RT) #math-ph #math.MP #math.RT #msc:22E70 #msc:35Q41
paper · pdf · doi:10.48550/arxiv.1104.3508
arxiv created 2011/04/18 · openalex publication_date 2011/04/18 · arxiv updated 2011/04/19 · openalex created_date 2022/08/30 · openalex updated_date 2026/07/28
We study the representation theory of the solution space of the one-dimensional Schrödinger equation with time-dependent potentials that posses \mathfraksl2-symmetry. We give explicit local intertwining maps to multiplier representations and show that the study of the solution space for potentials of the form V(t,x)=g2(t)x2+g1(t)x+g0(t) reduces to the study of the potential free case. We also show that the study of the time-dependent potentials of the form V(t,x)=λx-2+g2(t)x2+g0(t) reduces to the study of the potential V(t,x)=λx-2. Therefore, we study the representation theory associated to solutions of the Schrödinger equation with this potential. The subspace of solutions for which the action globalizes is constructed via nonstandard induction outside the semisimple category.