The matching pursuit split operator Fourier transform (MP/SOFT) method will be presented as a rigorous and practical methodology for quantum propagation of wave packets and density matrices. MP/SOFT recursively applies the time-evolution operator, as defined by the Trotter expansion to second order accuracy, in dynamically adaptive
coherent-state representations generated by a sequential orthogonal decomposition scheme inspired in the matching-pursuit algorithm. Applications will include adiabatic and nonadiabatic dynamics of molecular systems by integration of the time-dependent Schrödinger equation, and calculations of thermal correlation functions by solving the Bloch equation via imaginary-time propagation of the density matrix, and evaluating Heisenberg time-evolution operators through real-time propagation.
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