ListarDepartament: Matemàtiques por tema "Magnus expansion"

A pedagogical approach to the Magnus expansion

Blanes, Sergio; Casas, Fernando; Oteo, J. A.; Ros, J. Institute of Physics (2010-07)

Time-dependent perturbation theory as a tool to compute approximate solutions of the Schrödinger equation does not preserve unitarity. Here we present, in a simple way, how the Magnus expansion (also known as exponential ...

Efficient numerical integration of NNth-order non-autonomous linear differential equations

Bader, Philipp; Blanes, Sergio; Casas, Fernando; Ponsoda, Enrique Elsevier (2016)

We consider the numerical integration of high-order linear non-homogeneous differential equations, written as first order homogeneous linear equations, and using exponential methods. Integrators like Magnus expansions or ...

Exponential Perturbative Expansions and Coordinate Transformations

Arnal, A.; Casas, Fernando; Chiralt, Cristina MDPI (2020)

We propose a unified approach for different exponential perturbation techniques used in the treatment of time-dependent quantum mechanical problems, namely the Magnus expansion, the Floquet–Magnus expansion for periodic ...

New anallytic approximations based on the Magnus expansion

Sánchez, S.; Casas, Fernando; Fernández, A. Springer Science+Business Media, LLC (2011-09)

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 ...

Unitary transformations depending on a small parameter

Casas, Fernando; Oteo, J. A.; Ros, J. Royal Society, The (2012)

We formulate a unitary perturbation theory for quantum mechanics inspired by the LieDeprit formulation of canonical transformations. The original Hamiltonian is converted into a solvable one by a transformation obtained ...