A Stochastic Mechanics Based on Bohm?s Theory and its Connection with Quantum Mechanics |
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Authors: | Boon Leong Lan Ying Oon Tan |
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Institution: | (1) School of Engineering, Monash University, 2 Jalan Kolej, 46150, Selangor, Malaysia |
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Abstract: | We construct a stochastic mechanics by replacing Bohm‧s first-order ordinary differential equation of motion with a stochastic
differential equation where the stochastic process is defined by the set of Bohmian momentum time histories from an ensemble
of particles. We show that, if the stochastic process is a purely random process with n-th order joint probability density in the form of products of delta functions, then the stochastic mechanics is equivalent
to quantum mechanics in the sense that the former yields the same position probability density as the latter. However, for
a particular non-purely random process, we show that the stochastic mechanics is not equivalent to quantum mechanics. Whether
the equivalence between the stochastic mechanics and quantum mechanics holds for all purely random processes but breaks down for all non-purely random processes remains an open question. |
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Keywords: | Bohmian mechanics stochastic differential equation stochastic process |
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