2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/203915Newton-Hooke group is the nonrelativistic limit of de Sitter (anti-de Sitter) group, which can be enlarged with transformations that describe constant acceleration, as well as central charges. We consider a higher order Lagrangian that is quasi-invariant under the acceleration-extended Newton-Hooke symmetry, and obtain the Schrödinger equation quantizing the Hamiltonian corresponding to its first order form. We show that the Schrödinger equation is invariant under the acceleration-extended Newton-Hooke transformations. We also discuss briefly the exotic conformal Newton-Hooke symmetry in 2+1 dimension.14 pages, revtex4; refs added, misleading statements revised, version to appear in Phys. Lett. AHigh Energy Physics - Theorytext