New analytic approximations based on the Magnus expansion

The Magnus expansion is a frequently used tool to get approximate analytic solutions of time-dependent linear ordinary differential equations and in particular the Schrödinger equation in quantum mechanics. However, the complexity of the expansion restricts its use in practice only to the first terms. Here we introduce new and more accurate analytic approximations based on the Magnus expansion involving only univariate integrals which also shares with the exact solution its main qualitative and geometric properties. Facultad de Matemática y Computación, Universidad de Oriente, Ave. Patricio Lumumba s/n, Santiago de Cuba, Cuba. Institut de Matemàtiques i Aplicacions de Castelló and Departament de Matemàtiques, Universitat Jaume I, E-12071 Castellón, Spain.