Book•
The Principles of Quantum Mechanics
01 Jan 1930-
About: The article was published on 1930-01-01 and is currently open access. It has received 5991 citations till now. The article focuses on the topics: Quantum statistical mechanics & Open quantum system.
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754 citations
Book•
26 Jul 2012TL;DR: The foundations for modelling probabilistic-dynamic systems using two aspects of quantum theory, 'contextuality' and 'quantum entanglement', are introduced, which allow cognitive phenomena to be modeled in non-reductionist ways.
Abstract: Much of our understanding of human thinking is based on probabilistic models. This innovative book by Jerome R. Busemeyer and Peter D. Bruza argues that, actually, the underlying mathematical structures from quantum theory provide a much better account of human thinking than traditional models. They introduce the foundations for modelling probabilistic-dynamic systems using two aspects of quantum theory. The first, 'contextuality', is a way to understand interference effects found with inferences and decisions under conditions of uncertainty. The second, 'quantum entanglement', allows cognitive phenomena to be modeled in non-reductionist ways. Employing these principles drawn from quantum theory allows us to view human cognition and decision in a totally new light. Introducing the basic principles in an easy-to-follow way, this book does not assume a physics background or a quantum brain and comes complete with a tutorial and fully worked-out applications in important areas of cognition and decision.
745 citations
TL;DR: The toy theory of as discussed by the authors states that the number of questions about the physical state of a system that are answered must always be equal to the number that are unanswered in a state of maximal knowledge.
Abstract: We present a toy theory that is based on a simple principle: the number of questions about the physical state of a system that are answered must always be equal to the number that are unanswered in a state of maximal knowledge. Many quantum phenomena are found to have analogues within this toy theory. These include the noncommutativity of measurements, interference, the multiplicity of convex decompositions of a mixed state, the impossibility of discriminating nonorthogonal states, the impossibility of a universal state inverter, the distinction between bipartite and tripartite entanglement, the monogamy of pure entanglement, no cloning, no broadcasting, remote steering, teleportation, entanglement swapping, dense coding, mutually unbiased bases, and many others. The diversity and quality of these analogies is taken as evidence for the view that quantum states are states of incomplete knowledge rather than states of reality. A consideration of the phenomena that the toy theory fails to reproduce, notably, violations of Bell inequalities and the existence of a Kochen-Specker theorem, provides clues for how to proceed with this research program.
726 citations
TL;DR: In this paper, a generalization of classical mechanics is presented, where dynamical variables (functions on the phase space) are assumed to be elements of an algebra with anticommuting generators (the Grassmann algebra).
717 citations
TL;DR: In this paper, the authors place the Thomas-Fermi model of the quantum theory of atoms, molecules, and solids on a firm mathematical footing and show that the quantum mechanical energy is asymptotic to the Thomas Fermi energy.
671 citations