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Quantum initial value representations using approximate Bohmian trajectories

Eric R. Bittner
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Abstract

Quantum trajectories, originating from the de Broglie-Bohm (dBB) hydrodynamic description of quantum mechanics, are used to construct time-correlation functions in an initial value representation (IVR). The formulation is fully quantum mechanical and the resulting equations for the correlation functions are similar in form to their semi-classical analogs but do not require the computation of the stability or monodromy matrix or conjugate points. We then move to a {\em local} trajectory description by evolving the cumulants of the wave function along each individual path. The resulting equations of motion are an infinite hierarchy, which we truncate at a given order. We show that time-correlation functions computed using these approximate quantum trajectories can be used to accurately compute the eigenvalue spectrum for various potential systems.

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Eric R. Bittner. 2003-04-02. Quantum initial value representations using approximate Bohmian trajectories. https://doi.org/10.1063/1.1580471

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