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Full-Text Articles in Biological and Chemical Physics
Bohmian Dynamics On Subspaces Using Linearized Quantum Force, V. A. Rassolov, Sophya V. Garashchuk
Bohmian Dynamics On Subspaces Using Linearized Quantum Force, V. A. Rassolov, Sophya V. Garashchuk
Faculty Publications
In the de Broglie–Bohm formulation of quantum mechanics the time-dependent Schrödinger equation is solved in terms of quantum trajectories evolving under the influence of quantum and classical potentials. For a practical implementation that scales favorably with system size and is accurate for semiclassical systems, we use approximate quantum potentials. Recently, we have shown that optimization of the nonclassical component of the momentum operator in terms of fitting functions leads to the energy-conserving approximate quantum potential. In particular, linear fitting functions give the exact time evolution of a Gaussian wave packet in a locally quadratic potential and can describe the dominant …
Semiclassical Dynamics With Quantum Trajectories: Formulation And Comparison With The Semiclassical Initial Value Representation Propagator, Sophya V. Garashchuk, V. A. Rassolov
Semiclassical Dynamics With Quantum Trajectories: Formulation And Comparison With The Semiclassical Initial Value Representation Propagator, Sophya V. Garashchuk, V. A. Rassolov
Faculty Publications
We present a time-dependent semiclassical method based on quantum trajectories. Quantum-mechanical effects are described via the quantum potential computed from the wave function density approximated as a linear combination of Gaussian fitting functions. The number of the fitting functions determines the accuracy of the approximate quantum potential (AQP). One Gaussian fit reproduces time-evolution of a Gaussian wave packet in a parabolic potential. The limit of the large number of fitting Gaussians and trajectories gives the full quantum-mechanical result. The method is systematically improvable from classical to fully quantum. The fitting procedure is implemented as a gradient minimization. We also compare …