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Many-Body Systems and Quantum Hydrodynamics

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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

The problem of many-body interactions—or, equivalently, many degrees of freedom—can be tackled from different points of view, since it appears in many different physical and chemical contexts. Here, in particular, we are going to face it from a chemical physics point of view. The application of the Schrödinger equation to discern electronic structural properties of materials is commonly regarded as quantum chemistry (i.e., electronic structure and its methodology), while the dynamical and statistical part of the theoretical chemistry are the subjects of chemical physics. In this chapter, first we introduce the Born-Oppenheimer approximation used both to devise electronic structure methodologies and to deal with many degree-of-freedom systems within the open quantum theory scenario. Then, a brief overview on density functional theory, both time-independent and time-dependent, with special emphasis on the quantum hydrodynamic approach, strongly connected to Bohmian mechanics (and more specifically to Madelung’s quantum hydrodynamics) is presented. Finally, a description of Hirschfelder’s approach to quantum equations of change is reported, which are a precedent to the so-called weak values. The chapter is ended with a general discussion on the possibility to connect particular sectors of the initial state with individual features of the final state by means of probability tubes defined following the prescriptions of Bohmian mechanics.

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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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Sanz, Á.S., Miret-Artés, S. (2014). Many-Body Systems and Quantum Hydrodynamics. 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_8

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