Quantum Equilibrium and the Role of Operators as Observables in Quantum Theory

@article{Drr2003QuantumEA,
  title={Quantum Equilibrium and the Role of Operators as Observables in Quantum Theory},
  author={Detlef D{\"u}rr and Sheldon Goldstein and Nino Zangh{\'i}},
  journal={Journal of Statistical Physics},
  year={2003},
  volume={116},
  pages={959-1055}
}
Bohmian mechanics is arguably the most naively obvious embedding imaginable of Schrödinger'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 ψits configuration is… 
View on Springer
arxiv.org
146 Citations
Highly Influential Citations
8
Background Citations
47
Methods Citations
11
Results Citations
2

146 Citations

Citation Type

Citation Type

Semi-classical approximations based on Bohmian mechanics
Semi-classical theories are approximations to quantum theory that treat some degrees of freedom classically and others quantum mechanically. In the usual approach, the quantum degrees of freedom are…
Quantum and semiclassical dynamics as fluid theories where gauge matters
The family of trajectories-based approximations employed in computational quantum physics and chemistry is very diverse. For instance, Bohmian and Heller's frozen Gaussian semiclassical trajectories…
Time in quantum mechanics: A fresh look on quantum hydrodynamics and quantum trajectories
Quantum hydrodynamics is a formulation of quantum mechanics based on the probability density and flux (current) density of a quantum system. It can be used to define trajectories which allow for a…
Outline of Quantum Mechanics
This is a brief outline of the mathematics of quantum mechanics. It begins with examples of unitary time evolution given by the Schrödinger equation. It is then shown how the spectral theorem for…
Epistemology of Wave Function Collapse in Quantum Physics
Among several possibilities for what reality could be like in view of the empirical facts of quantum mechanics, one is provided by theories of spontaneous wave function collapse, the best known of…
Reality and the Role of the Wavefunction in Quantum Theory
The most puzzling issue in the foundations of quantum mechanics is perhaps that of the status of the wave function of a system in a quantum universe. Is the wave function objective or subjective?…
Applied Bohmian mechanics
Abstract Bohmian mechanics provides an explanation of quantum phenomena in terms of point-like particles guided by wave functions. This review focuses on the use of nonrelativistic Bohmian mechanics…
Cosmological models with asymmetric quantum bounces
In quantum cosmology, one has to select a specific wave function solution of the quantum state equations under consideration in order to obtain concrete results. The simplest choices have been…
Bohmian Mechanics and Quantum Information
Many recent results suggest that quantum theory is about information, and that quantum theory is best understood as arising from principles concerning information and information processing. At the…
On Relativistic Interactions in Quantum Theories
  • Physics
  • 2015
This thesis is dedicated to the question: (How) Is a relativistic quantum theory with interaction possible? We discuss the problems of quantum field theories, especially the non-existence of…
...
...

References

SHOWING 1-10 OF 102 REFERENCES
Quantum equilibrium and the origin of absolute uncertainty
The quantum formalism is a “measurement” formalism-a phenomenological formalism describing certain macroscopic regularities. We argue that it can be regarded, and best be understood, as arising from…
Quantum Mechanics in the Light of Quantum Cosmology
We sketch a quantum mechanical framework for the universe as a whole. Within that framework we propose a program for describing the ultimate origin in quantum cosmology of the quasiclassical domain…
On the Wave Function of the Photon
It is believed that certain matrix elements of the electromagnetic field operators in quantum electrodynamics, in close analogy with nonrelativistic quantum theory of massive particles, may be…
Mathematical Foundations of Quantum Mechanics
Mathematical Foundations of Quantum Mechanics was a revolutionary book that caused a sea change in theoretical physics. Here, John von Neumann, one of the leading mathematicians of the twentieth…
On the Role of Density Matrices in Bohmian Mechanics
It is well known that density matrices can be used in quantum mechanics to represent the information available to an observer about either a system with a random wave function (“statistical mixture”)…
Logical reformulation of quantum mechanics. I. Foundations
The basic rules of quantum mechanics are reformulated. They deal primarily with individual systems and do not assume that every ket may represent a physical state. The customary kinematic and dynamic…
Environment-induced superselection rules
We show how the correlations of a quantum system with other quantum systems may cause one of its observables to behave in a classical manner. In particular, "reduction of the wave packet," postulated…
The emergence of classical properties through interaction with the environment
The dependence of macroscopic systems upon their environment is studied under the assumption that quantum theory is universally valid. In particular scattering of photons and molecules turns out to…
Old and New Ideas in the Theory of Quantum Measurement
The conceptually simplest interpretation of the quantum-mechanical wave function is that adopted by most textbooks. In the celebrated book by Dirac1 one reads — each state of a dynamical system at a…
Stochastic mechanics and quantum theory
Stochastic mechanics may be regarded as both generalizing classical mechanics to processes with intrinsic randomness, as well as providing the sort of detailed description of microscopic events…
...
...