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Communication: Quantum mechanics without wavefunctions
1. J. von Neumann, Mathematical Foundations of Quantum Mechanics (Princeton University Press, Princeton, NJ, 1932).
3. P. R. Holland, The Quantum Theory of Motion (Cambridge University Press, Cambridge, England, 1993).
4. R. E. Wyatt, Quantum Dynamics with Trajectories: Introduction to Quantum Hydrodynamics (Springer, New York, 2005).
11. G. Parlant, Y.-C. Ou, K. Park, and B. Poirier, “Classical-like trajectory simulations for accurate computation of quantum reactive scattering probabilities,” Comput. Theor. Chem. (in press).
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We present a self-contained formulation of spin-free non-relativistic quantum mechanics that makes no use of wavefunctions or complex amplitudes of any kind. Quantum states are represented as ensembles of real-valued quantum trajectories, obtained by extremizing an action and satisfying energy conservation. The theory applies for arbitrary configuration spaces and system dimensionalities. Various beneficial ramifications—theoretical, computational, and interpretational—are discussed.
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