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A Survey of Bohmian Mechanics

Karin Berndl, M. Daumer, Sheldon Goldstein +4 more

Bohmian mechanics is the most naively obvious embedding imaginable of Schr\\"odinger's equation into a completely coherent physical theory. It describes a world in which particles move in a highly non-Newtonian sort of way, one which may at first appear to have little to do with the spectrum of predictions of quantum mechanics. It turns out, however, that as a consequence of the defining dynamical equations of Bohmian mechanics, when a system has wave function \\psi its configuration is typically random, with probability density \\rho given by |\\psi|^2, the quantum equilibrium distribution. It also turns out that the entire quantum formalism, operators as observables and all the rest, is a consequence of Bohmian mechanics.Bohmian mechanics is the most naively obvious embedding imaginable of Schr\\"odinger's equation into a completely coherent physical theory. It describes a world in which particles move in a highly non-Newtonian sort of way, one which may at first appear to have little to do with the spectrum of predictions of quantum mechanics. It turns out, however, that as a consequence of the defining dynamical equations of Bohmian mechanics, when a system has wave function \\psi its configuration is typically random, with probability density \\rho given by |\\psi|^2, the quantum equilibrium distribution. It also turns out that the entire quantum formalism, operators as observables and all the rest, is a consequence of Bohmian mechanics.

Jan 1, 199568 citations

Overview of Bohmian Mechanics

Xavier Oriols

Pan Stanford Publishing eBooksJun 4, 201217 citations

Alternative Interpretations of Quantum Mechanics

David W. Snoke

Given the philosophical problems of the Copenhagen interpretation, several other approaches to interpreting quantum mechanics have been proposed over the years. This chapter surveys four of these approaches, namely the many-worlds hypothesis, Bohmian “pilot waves,” positivist approaches, and spontaneous collapse of the quantum wave function. Problems with each of these approaches are discussed.

Cambridge University Press eBooksApr 30, 20240 citations

Overview of Bohmian Mechanics

J. I. Cirac

Jan 1, 20120 citations

Bohmian Mechanics Revisited

E. Deotto, G. C. Ghirardi

arXiv:quant-ph/9704021Foundations of PhysicsJan 1, 1998145 citations

Reformulation of Bohmian mechanics

Moise Borilla Licea

Bohmian mechanics as formulated originally in 1952, has been useful in the implementation of numerical methods applied to quantum mechanics. The scientific community though has had ever since a critical thought about it. Therefore, there are still points to be clarified and rectified. The two main problems are basically: Bohmian mechanics gives a privilege role to the position representation. Secondly, the current interpretation of Bohmian trajectories has been recently proven wrong. In this context, in Chapter 2, new complex Bohmian quantities are defined; so that they allow the capacity to formulate Bohmian mechanics in any arbitrary continuous representation, for instance, the momentum representation. This Chapter is fully based on two articles, regarding the proposed complex Bohmian formulation and its extension into momentum space. Chapter 3 deals with a redefinition and reinterpretation of the Bohmian trajectories from the handling of the continuity equation, this is done without any need of additional postulates or interpretations. Also, it is proved that Bohmian mechanics is actually more than a projective aspect of the Wigner function. As a third point, Chapter 4 presents a sytematic treatment of the hydrodynamic scheme of Bohmian mechanics. Then, a brief summary of the transport equations in Bohmian mechanics is done. Next, a unified hydrodynamic treatment is found for the Bohmian mechanics. This treatment is useful to sketch, a Bohmian treatment to efficiently find the steady value of the transmission integral. In Chapter 5 conclusions of this thesis are drawn.Bohmian mechanics as formulated originally in 1952, has been useful in the implementation of numerical methods applied to quantum mechanics. The scientific community though has had ever since a critical thought about it. Therefore, there are still points to be clarified and rectified. The two main problems are basically: Bohmian mechanics gives a privilege role to the position representation. Secondly, the current interpretation of Bohmian trajectories has been recently proven wrong. In this context, in Chapter 2, new complex Bohmian quantities are defined; so that they allow the capacity to formulate Bohmian mechanics in any arbitrary continuous representation, for instance, the momentum representation. This Chapter is fully based on two articles, regarding the proposed complex Bohmian formulation and its extension into momentum space. Chapter 3 deals with a redefinition and reinterpretation of the Bohmian trajectories from the handling of the continuity equation, this is done without any need of additional postulates or interpretations. Also, it is proved that Bohmian mechanics is actually more than a projective aspect of the Wigner function. As a third point, Chapter 4 presents a sytematic treatment of the hydrodynamic scheme of Bohmian mechanics. Then, a brief summary of the transport equations in Bohmian mechanics is done. Next, a unified hydrodynamic treatment is found for the Bohmian mechanics. This treatment is useful to sketch, a Bohmian treatment to efficiently find the steady value of the transmission integral. In Chapter 5 conclusions of this thesis are drawn.

Jan 1, 20210 citations

A survey of Bohmian mechanics

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