Space-Time Approach to Non-Relativistic Quantum Mechanics
Reads0
Chats0
TLDR
In this paper, the authors formulated non-relativistic quantum mechanics in a different way and showed that 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.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.read more
Citations
More filters
Journal ArticleDOI
Keldysh Field Theory for Driven Open Quantum Systems
TL;DR: This work provides a systematic introduction to the open system Keldysh functional integral approach, which is the proper technical tool to accomplish a merger of quantum optics and many-body physics, and leverages the power of modern quantum field theory to driven open quantum systems.
Journal ArticleDOI
GPU computing for accelerating the numerical Path Integration approach
TL;DR: The paper discusses a novel approach of accelerating the numerical Path Integration method, used for generating a stationary joint response probability density function of a dynamic system subjected to a random excitation, by the GPU computing.
Journal ArticleDOI
Potential theory, path integrals and the Laplacian of the indicator
TL;DR: In this paper, the authors connect the field of potential theory to that of the Feynman path integral by postulating that the potential is equal to plus/minus the Laplacian of the indicator of the domain D. This function has not formally been defined before.
Journal ArticleDOI
Coulomb Potentials by Path Integration
TL;DR: In this paper, the path integral for the Coulomb potential was evaluated in three different coordinate systems, i.e., in cartesian coordinates, in polar coordinates and in parabolic coordinates.
Posted Content
Analyzing Stochastic Computer Models: A Review with Opportunities
Evan Baker,Pierre Barbillon,Arindam Fadikar,Robert B. Gramacy,Radu Herbei,David Higdon,Jiangeng Huang,Leah R. Johnson,Pulong Ma,Anirban Mondal,Bianica Pires,Jerome Sacks,Vadim Sokolov +12 more
TL;DR: This review aims to bring a spotlight to the growing prevalence of stochastic computer models -- providing a catalogue of statistical methods for practitioners, an introductory view for statisticians, and an emphasis on open questions of relevance to practitioners and statisticians.