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Full-Text Articles in Physical Sciences and Mathematics
Bohmian Dynamics On Subspaces Using Linearized Quantum Force, Vitaly A. Rassolov, Sophya Garashchuk
Bohmian Dynamics On Subspaces Using Linearized Quantum Force, Vitaly A. Rassolov, Sophya 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 …
Energy Conserving Approximations To The Quantum Potential: Dynamics With Linearized Quantum Force, Sophya Garashchuk, Vitaly A. Rassolov
Energy Conserving Approximations To The Quantum Potential: Dynamics With Linearized Quantum Force, Sophya Garashchuk, Vitaly A. Rassolov
Faculty Publications
Solution of the Schrödinger equation within the de Broglie–Bohm formulation is based on propagation of trajectories in the presence of a nonlocal quantum potential. We present a new strategy for defining approximate quantum potentials within a restricted trial function by performing the optimal fit to the log-derivatives of the wave function density. This procedure results in the energy-conserving dynamics for a closed system. For one particular form of the trial function leading to the linear quantum force, the optimization problem is solved analytically in terms of the first and second moments of the weighted trajectory distribution. This approach gives exact …