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Quantum probability

About: Quantum probability is a(n) research topic. Over the lifetime, 7519 publication(s) have been published within this topic receiving 263350 citation(s).
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01 Jan 1965-
Abstract: Au sommaire : 1.The fundamental concepts of quantum mechanics ; 2.The quantum-mechanical law of motion ; 3.Developing the concepts with special examples ; 4.The schrodinger description of quantum mechanics ; 5.Measurements and operators ; 6.The perturbation method in quantum mechanics ; 7.Transition elements ; 8.Harmonic oscillators ; 9.Quantum electrodynamics ; 10.Statistical mechanics ; 11.The variational method ; 12.Other problems in probability.

7,993 citations

29 Aug 2002-
Abstract: PREFACE ACKNOWLEDGEMENTS PART 1: PROBABILITY IN CLASSICAL AND QUANTUM MECHANICS 1. Classical probability theory and stochastic processes 2. Quantum Probability PART 2: DENSITY MATRIX THEORY 3. Quantum Master Equations 4. Decoherence PART 3: STOCHASTIC PROCESSES IN HILBERT SPACE 5. Probability distributions on Hilbert space 6. Stochastic dynamics in Hilbert space 7. The stochastic simulation method 8. Applications to quantum optical systems PART 4: NON-MARKOVIAN QUANTUM PROCESSES 9. Projection operator techniques 10. Non-Markovian dynamics in physical systems PART 5: RELATIVISTIC QUANTUM PROCESSES 11. Measurements in relativistic quantum mechanics 12. Open quantum electrodynamics

5,810 citations

Journal ArticleDOI
Abstract: The notion of a quantum dynamical semigroup is defined using the concept of a completely positive map. An explicit form of a bounded generator of such a semigroup onB(ℋ) is derived. This is a quantum analogue of the Levy-Khinchin formula. As a result the general form of a large class of Markovian quantum-mechanical master equations is obtained.

5,485 citations

01 Jan 1955-
Abstract: 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 century, shows that great insights in quantum physics can be obtained by exploring the mathematical structure of quantum mechanics. He begins by presenting the theory of Hermitean operators and Hilbert spaces. These provide the framework for transformation theory, which von Neumann regards as the definitive form of quantum mechanics. Using this theory, he attacks with mathematical rigor some of the general problems of quantum theory, such as quantum statistical mechanics as well as measurement processes. Regarded as a tour de force at the time of publication, this book is still indispensable for those interested in the fundamental issues of quantum mechanics.

4,880 citations

Journal ArticleDOI
Abstract: Non-relativistic quantum mechanics is formulated here in a different way. It is, however, mathematically equivalent to the familiar formulation. In quantum mechanics the probability of an event which can happen in several different ways is the absolute square of a sum of complex contributions, one from each alternative way. The probability that a particle will be found to have a path x(t) lying somewhere within a region of space time is the square of a sum of contributions, one from each path in the region. The contribution from a single path is postulated to be an exponential whose (imaginary) phase is the classical action (in units of ℏ) for the path in question. The total contribution from all paths reaching x, t from the past is the wave function ψ(x, t). This is shown to satisfy Schroedinger's equation. The relation to matrix and operator algebra is discussed. Applications are indicated, in particular to eliminate the coordinates of the field oscillators from the equations of quantum electrodynamics.

3,470 citations

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Topic's top 5 most impactful authors

Andrei Khrennikov

87 papers, 1.7K citations

Luigi Accardi

71 papers, 1.2K citations

Jerome R. Busemeyer

33 papers, 3.1K citations

Viacheslav P. Belavkin

28 papers, 766 citations

Alberto Barchielli

25 papers, 1K citations