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✔ Reconciling Semiclassical and Bohmian Mechanics: III. Scattering states for continuous potentials

  [CiTO]
(27 Feb 2008)
by Corey Trahan, Bill Poirier
posted to quantum_mechanics by kriskrogh on 2008-02-28 06:41:48 **
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Abstract

In a previous paper [J. Chem. Phys. 121 4501 (2004)] a unique bipolar decomposition, Psi = Psi1 + Psi2 was presented for stationary bound states Psi of the one-dimensional Schroedinger equation, such that the components Psi1 and Psi2 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 Psi has many nodes, or is wildly oscillatory. A modification for discontinuous potential stationary stattering states was presented in a second ...
 

✔ Reconciling Semiclassical and Bohmian Mechanics: II. Scattering states for discontinuous potentials

  [CiTO]
(27 Feb 2008)
by Corey Trahan, Bill Poirier
posted to quantum_mechanics by kriskrogh on 2008-02-28 06:41:17 **
Abstract Copy My Attachments My Copy

Abstract

In a previous paper [J. Chem. Phys. 121 4501 (2004)] a unique bipolar decomposition, Psi = Psi1 + Psi2 was presented for stationary bound states Psi of the one-dimensional Schroedinger equation, such that the components Psi1 and Psi2 approach their semiclassical WKB analogs in the large action limit. Moreover, by applying the Madelung-Bohm ansatz to the components rather than to Psi itself, the resultant bipolar Bohmian mechanical formulation satisfies the correspondence principle. As a result, the bipolar quantum trajectories are classical-like and well-behaved, even when Psi has many ...
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