2008/11/26 by José F. Cariñena, Javier de Lucas, Arturo Ramos
Mathematics · Physics and Astronomy · #Adjoint representation of a Lie algebra #Algebra over a field #Geometry #Hamiltonian (control theory) #Imaginary time #Lie conformal algebra #Lie group #Lie theory #Mathematical optimization #Mathematical physics #Mathematics #Nonlinear Photonic Systems #Nonlinear Waves and Solitons #Physics #Pure mathematics #Quadratic equation #Quantum #Quantum Mechanics and Non-Hermitian Physics #Quantum dynamics #Quantum mechanics #Supersymmetric quantum mechanics #Time evolution #hep-th #math-ph #math.MP #msc:34A26
paper · pdf · doi:10.1007/s10773-008-9909-5
published as Int. J. Theor. Phys. Volume 48, Issue5 (2009), Page 1379. · Accepted for publication in the International Journal of Theoretical Physics
arxiv created 2008/11/26 · openalex publication_date 2008/12/03 · arxiv updated 2009/12/01 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05
Lie systems in Quantum Mechanics are studied from a geometric point of view. In particular, we develop methods to obtain time evolution operators of time-dependent Schrodinger equations of Lie type and we show how these methods explain certain ad hoc methods used in previous papers in order to obtain exact solutions. Finally, several instances of time-dependent quadratic Hamiltonian are solved.