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Bound System Dynamics

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A Trajectory Description of Quantum Processes. II. Applications

Part of the book series: Lecture Notes in Physics ((LNP,volume 831))

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Abstract

Up to now we have considered quantum systems which are not subject to any external force except for open systems. Such systems are usually associated with translational properties. On the contrary, bound systems generally describe properties related to some internal degrees of freedom (e.g., vibrations, rotations, absorption and emission processes, etc.), which have associated some quantization condition. In this chapter we want to analyze the dynamics of these systems, stressing the fact that not always the concept of trajectories must be understood as describing the evolution of a particle, but it can also refer to some other property. It is quite common to establish such a connection between trajectory and particle, even though the former, strictly speaking, makes reference to the solution of an equation of motion (or alternatively, within a hydrodynamic context, a flow equation). As paradigmatic examples, the harmonic oscillator as well as the nonlinear van der Pol oscillator are analyzed. Finally, in order to deal with nonconventional quantum states, such as quantum fractals, a generalization of Bohmian mechanics is also provided.

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Notes

  1. 1.

    Strictly speaking, the wave function (4.47) is a semi-fractal [49] or pre-fractal [50], since it is derived from a convergent series. Pre-fractals are characterized by having a fractal first derivative.

  2. 2.

    The concept of fractal quantum carpet [49] arises from the term quantum carpet (see Chap. 3), which describes the (D+1)-dimensional spacetime patterns generated by (regular) wave functions due to interference (see, for example, [40]).

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  1. Instituto de Física Fundamental (IFF-CSIC), CSIC, Madrid, Spain

    Dr. Ángel S. Sanz & Prof. Salvador Miret-Artés

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  1. Dr. Ángel S. Sanz
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  2. Prof. Salvador Miret-Artés
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Sanz, Á.S., Miret-Artés, S. (2014). Bound System Dynamics. In: A Trajectory Description of Quantum Processes. II. Applications. Lecture Notes in Physics, vol 831. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-17974-7_4

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