Applicability Criterion for Semiclassical Bohmian Dynamics

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In this paper we develop a criterion of the applicability for the trajectory-based semiclassical propagation methods that are exact for Gaussian wavepackets in locally quadratic potentials. The error estimate takes into account a deviation of the wavefunction from the Gaussian form due to the anharmonicity of a potential. The derivation is based on the time-dependent noncoherent solutions of the Schrödinger equation for a general quadratic potential that form a complete orthonormal time-dependent basis. The anharmonicity is treated as a time-dependent cubic perturbation, which is further related to the nonlinearity of a force acting on trajectories. The criterion is expressed in terms of scalar products of the average force, its first moments, and dispersion of the wavefunction and is efficient in the context of dynamics with the Bohmian trajectories. We give an application for the Bohmian dynamics with the approximate quantum potential, for the Gaussian wavepacket dynamics and for the semiclassical initial value representation propagator.