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Extra info for Adiabatic quantum transport.
The Bohmian approach to molecular quantum dynamics has recently been considered by Wyatt  and coworkers, as well as Askar and coworkers . Problems with the long time stability of the solution have been discussed in  and, at least at present, the extension to many dimensions poses some problems. Solution techniques in terms of distributed approximating functions (DAFs) have been presented in ref. . The quantum trajectory approach as deﬁned by the Bohmian mechanics is conceptually appealing in the sense that the limit to classical mechanics is well deﬁned and well behaved—it can be introduced simply by scaling the quantum potential with a scaling parameter between zero and unity.
4(−2) 52 The Quantum Classical Theory Since the classical path approximation is based on using just the ground state n1 = 0 for the R-degree of freedom, we can introduce the so-called Hermite correction to the classical path approximation by adding more G-H functions. This method has also been used in reactive scattering formulated in hyper-spherical coordinates (see ref.  and chapter 3). The Hermite correction corrects in a systematic way for the correlation, which due to the separability approximation in the classical path theory, has been omitted (see, for example, eq.
189)). 1). Problems with this iterative procedure have been noticed , . It may, therefore, be more advantageous to formulate theories in which one avoids taking the strict classical limit but retains some uncertainty or spread in the wave function for the degrees of freedom, which are near the classical limit. Thus, the problem with the formulation given by the Pechukas theory is not that it is wrong. The problem is actually that it is right, meaning that it is the right solution but to the wrong problem.