A Stochastic Mechanics Based on Bohm‧s Theory and its Connection with Quantum Mechanics

2006 ◽  
Vol 19 (2) ◽  
pp. 143-155
Author(s):  
Boon Leong Lan ◽  
Ying Oon Tan
Keyword(s):  
Quantum Mechanics ◽  
Stochastic Mechanics

scholarly journals Quantum Mechanics and Stochastic Mechanics for Compatible Observables at Different Times

2002 ◽  
Vol 296 (2) ◽  
pp. 371-389 ◽  
Author(s):  
M. Correggi ◽  
G. Morchio
Keyword(s):  
Quantum Mechanics ◽  
Stochastic Mechanics

scholarly journals Quantum Trajectories in Entropic Dynamics

Proceedings ◽  
2019 ◽  
Vol 33 (1) ◽  
pp. 25
Author(s):  
Nicholas Carrara
Keyword(s):  
Quantum Mechanics ◽  
Stochastic Equation ◽  
Bohmian Mechanics ◽  
Quantum Trajectories ◽  
Stochastic Mechanics ◽  
Scalar Particles ◽  
Double Slit ◽  
The Continuum ◽  
Entropic Dynamics

Entropic Dynamics is a framework for deriving the laws of physics from entropic inference. In an (ED) of particles, the central assumption is that particles have definite yet unknown positions. By appealing to certain symmetries, one can derive a quantum mechanics of scalar particles and particles with spin, in which the trajectories of the particles are given by a stochastic equation. This is much like Nelson’s stochastic mechanics which also assumes a fluctuating particle as the basis of the microstates. The uniqueness of ED as an entropic inference of particles allows one to continuously transition between fluctuating particles and the smooth trajectories assumed in Bohmian mechanics. In this work we explore the consequences of the ED framework by studying the trajectories of particles in the continuum between stochastic and Bohmian limits in the context of a few physical examples, which include the double slit and Stern-Gerlach experiments.

Can stochastic mechanics be equivalent to quantum mechanics?

2004 ◽  
Vol 51 (6-7) ◽  
pp. 1093-1094
Author(s):  
Boon Leong Lan ◽  
Ying Oon Tan
Keyword(s):  
Quantum Mechanics ◽  
Stochastic Mechanics

NELSON'S STOCHASTIC MECHANICS BY MEANS OF FEYNMAN PATH INTEGRALS

2000 ◽  
Vol 14 (03) ◽  
pp. 73-78 ◽  
Author(s):  
LUIZ C. L. BOTELHO
Keyword(s):  
Quantum Mechanics ◽  
Path Integral ◽  
Path Integrals ◽  
Order Equation ◽  
Feynman Path Integral ◽  
Stochastic Mechanics ◽  
Path Integral Formulation ◽  
Feynman Path ◽  
First Order ◽  
Feynman Path Integrals

We show that Nelson's stochastic mechanics suitably formulated as a Hamilton–Jacobi first-order equation leads straightforwardly to the Feynman path integral formulation of quantum mechanics.

scholarly journals On the Stochastic Mechanics Foundation of Quantum Mechanics

Universe ◽  
2021 ◽  
Vol 7 (6) ◽  
pp. 166
Author(s):  
Michael Beyer ◽  
Wolfgang Paul
Keyword(s):  
Quantum Mechanics ◽  
Diffusion Processes ◽  
Equations Of Motion ◽  
Kinetic Equations ◽  
Classical Mechanics ◽  
Stochastic Mechanics ◽  
Foundation Of Quantum Mechanics ◽  
Recent Developments ◽  
Quantum Phenomena ◽  
Quantum Mechanical Systems

Among the famous formulations of quantum mechanics, the stochastic picture developed since the middle of the last century remains one of the less known ones. It is possible to describe quantum mechanical systems with kinetic equations of motion in configuration space based on conservative diffusion processes. This leads to the representation of physical observables through stochastic processes instead of self-adjoint operators. The mathematical foundations of this approach were laid by Edward Nelson in 1966. It allows a different perspective on quantum phenomena without necessarily using the wave-function. This article recaps the development of stochastic mechanics with a focus on variational and extremal principles. Furthermore, based on recent developments of optimal control theory, the derivation of generalized canonical equations of motion for quantum systems within the stochastic picture are discussed. These so-called quantum Hamilton equations add another layer to the different formalisms from classical mechanics that find their counterpart in quantum mechanics.

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