New analytic approximations based on the Magnus expansion |
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Authors: | S Sánchez F Casas A Fernández |
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Institution: | (1) Department of Applied Mathematics and Theoretical Physics, University of Cambridge, Cambridge, CB3 9EW, England.;(2) Departament de Matemàtiques, Universitat Jaume I, 12071- Castellón, Spain.;(3) Departament de Física Teòrica and IFIC, Universitat de València, 46100- Burjassot, Valencia, Spain. |
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Abstract: | 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. |
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