Numerische Mathematik

, Volume 94, Issue 2, pp 289–314 | Cite as

Numerical integrators for quantum dynamics close to the adiabatic limit

  • Tobias Jahnke
  • Christian Lubich

Summary.

 We study the numerical solution of singularly perturbed Schrö-dinger equations with time-dependent Hamiltonian. Based on a reformulation of the equations, we derive time-reversible numerical integrators which can be used with step sizes that are substantially larger than with traditional integration schemes. A complete error analysis is given for the adiabatic case. To deal with avoided crossings of energy levels, which lead to non-adiabatic behaviour, we propose an adaptive extension of the methods which resolves the sharp transients that appear in non-adiabatic state transitions.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2003

Authors and Affiliations

  • Tobias Jahnke
    • 1
  • Christian Lubich
    • 1
  1. 1.Mathematisches Institut, Universität Tübingen, Auf der Morgenstelle 10, D-72076 Tübingen, Germany; e-mail: {jahnke, lubich}@na.uni-tuebingen.deDE

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