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We discuss the multi-configuration
time-dependent Hartree (MCTDH) method for the approximation
of the time-dependent Schrödinger equation in quantum molecular dynamics.
This method approximates the high-dimensional nuclear
wave function by a linear combination of products of functions depending
only on a single degree of freedom. The
equations of motion, obtained the Dirac-Frenkel
time-dependent variational principle,
consist of a coupled system of low-dimensional
nonlinear partial differential...
In this work, the error behaviour of high-order exponential operator splitting methods for the time integration of nonlinear evolutionary Schrödinger equations is investigated. The theoretical analysis utilises the framework of abstract evolution equations on Banach spaces and the formal calculus of Lie derivatives. The general approach is substantiated on the basis of a convergence result for exponential operator splitting methods of (nonstiff) order applied to the multi-configuration time-dependent...
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