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Abstract: The solution with respect to the reduced action of the one-dimensionalstationary quantum Hamilton-Jacobi equation is well known in the literature.The extension to higher dimensions in the separated variable case was proposedin contradictory formulations. In this paper we provide new insights into theconstruction of the reduced action. In particular, contrary to the classicalmechanics case, we analytically show that the reduced action constructed as asum of one variable functions does not contain a complete information about thequantum motion. In the same context, we also make some observations aboutrecent results concerning quantum trajectories. Finally, we will examine theconditions in which microstates appear even in the case where the wave functionis complex.



Author: A.Bouda

Source: https://arxiv.org/



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