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## Full-Text Articles in Physics

Energy Conserving Approximations To The Quantum Potential: Dynamics With Linearized Quantum Force, Sophya V. Garashchuk, V. A. Rassolov

#### Energy Conserving Approximations To The Quantum Potential: Dynamics With Linearized Quantum Force, Sophya V. Garashchuk, V. 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 ...

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 ...

Semiclassical Application Of The Mo/Ller Operators In Reactive Scattering, Sophya V. Garashchuk, J. C. Light

#### Semiclassical Application Of The Mo/Ller Operators In Reactive Scattering, Sophya V. Garashchuk, J. C. Light

*Faculty Publications*

Mo/ller operators in the formulation of reaction probabilities in terms of wave packet correlation functions allow us to define the wave packets in the interaction region rather than in the asymptotic region of the potential surface. We combine Mo/ller operators with the semiclassical propagator of Herman and Kluk. This does not involve further approximations and can be used with any initial value representation (IVR) semiclassical propagator. Time propagation in asymptotic regions of the potential due to Mo/ller operators reduces the oscillations of the propagator integrand and improves convergence of the results with respect to the number of ...

Cumulative Reaction Probability In Terms Of Reactant-Product Wave Packet Correlation Functions, Sophya V. Garashchuk, D. J. Tannor

#### Cumulative Reaction Probability In Terms Of Reactant-Product Wave Packet Correlation Functions, Sophya V. Garashchuk, D. J. Tannor

*Faculty Publications*

We present new expressions for the cumulative reaction probability (N(E)), cast in terms of time-correlation functions of reactant and product wave packets. The derivation begins with a standard trace expression for the cumulative reaction probability, expressed in terms of the reactive scattering matrix elements in an asymptotic internal basis. By combining the property of invariance of the trace with a wave packet correlation function formulation of reactive scattering, we obtain an expression for N(E) in terms of the correlation matrices of incoming and outgoing wave packets which are *arbitrary* in the internal coordinates. This formulation, like other recent ...