1991 | OriginalPaper | Buchkapitel
Stochastic Quantum Mechanics
verfasst von : R. Vasudevan
Erschienen in: Stochastic Processes and their Applications
Verlag: Springer Berlin Heidelberg
Enthalten in: Professional Book Archive
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The need for answering the question whether quantum mechanics is complete by itself and whether quantum fluctuations and thermal fluctuations are of the same genus, is discussed in this report. The hydrodynamic Hamilton Jacobi equations for the quantum Madelung fluid reveal the existence of a quantum potential which corresponds to the mysterious dependence of the individual on the statistical ensemble of which it is a member. Nelson’s analysis, starting from the Brownian motion of a particle moving in the field of a background white noise, leads to coupled equations for the velocity fields under certain conditions; these are described in the first three sections.Section 4 deals with indeterminacy relation in a novel way based on the two velocities envisaged in Nelson’s work and some examples are given. The concluding section deals with the criticism of these two approaches and promises the unification of the three approaches including the derivation of the Feynman’s path formalism obtained by complexifying the phase accumulation and assigning a proper measure for it. The extension of this approach to relativistic and spinning particles will form the content of part II of this article to be published elsewhere.