Numerical integrators for quantum dynamics close to the adiabatic limit
- Cite this article as:
- Jahnke, T. & Lubich, C. Numer. Math. (2003) 94: 289. doi:10.1007/s00211-002-0421-1
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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.