1. Reconciling semiclassical and Bohmian mechanics. III. Scattering states for continuous potentials.
- Author
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Trahan, Corey and Poirier, Bill
- Subjects
QUANTUM trajectories ,QUANTUM field theory ,ENERGY levels (Quantum mechanics) ,CHEMICAL decomposition ,SCHRODINGER equation ,PARTICLES (Nuclear physics) ,PHYSICS - Abstract
In a previous paper [B. Poirier, J. Chem. Phys. 121, 4501 (2004)] a unique bipolar decomposition Ψ=Ψ
1 +Ψ2 was presented for stationary bound states Ψ of the one-dimensional Schrödinger equation, such that the components Ψ1 and Ψ2 approach their semiclassical WKB analogs in the large-action limit. The corresponding bipolar quantum trajectories, as defined in the usual Bohmian mechanical formulation, are classical-like and well behaved, even when Ψ has many nodes or is wildly oscillatory. A modification for discontinuous potential stationary scattering states was presented in a second, companion paper [C. Trahan and B. Poirier, J. Chem. Phys.124, 034115 (2006), previous paper], whose generalization for continuous potentials is given here. The result is an exact quantum scattering methodology using classical trajectories. For additional convenience in handling the tunneling case, a constant-velocity-trajectory version is also developed. [ABSTRACT FROM AUTHOR]- Published
- 2006
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