One of the most accurate methods for solving the time-dependent Schrödinger equation
uses a combination of the dynamic Fourier method with the split-operator algorithm on a
tensor-product grid. To reduce the number of required grid points, we let the grid move
together with the wavepacket but find that the naïve algorithm based on an alternate
evolution of the wavefunction and grid destroys the time reversibility of the exact evolution.
Yet, we show that the time reversibility is recovered if the wavefunction and grid are evolved …