Publications Meetings The Profession Membership Programs Math Samplings Policy & Advocacy In the News About the AMS

Remote Access
Green Open Access
Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)


The stochastic mechanics of the Pauli equation

Author: Timothy C. Wallstrom
Journal: Trans. Amer. Math. Soc. 318 (1990), 749-762
MSC: Primary 81P20; Secondary 60J65
MathSciNet review: 986033
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: In stochastic mechanics, the Bopp-Haag-Dankel diffusions on $ {\mathbb{R}^3} \times \operatorname{SO} (3)$ are used to represent particles with spin. Bopp and Haag showed that in the limit as the particle's moment of inertia $ I$ goes to zero, the solutions of the Bopp-Haag equations converge to that of the regular Pauli equation. Nelson has conjectured that in the same limit, the projections of the Bopp-Haag-Dankel diffusions onto $ {\mathbb{R}^3}$ converge to a Markovian limit process. In this paper, we prove this conjecture for spin $ \operatorname{spin} \;\tfrac{1} {2}$ and regular potentials, and identify the limit process as the diffusion naturally associated with the solution to the regular Pauli equation.

References [Enhancements On Off] (What's this?)

Similar Articles

Retrieve articles in Transactions of the American Mathematical Society with MSC: 81P20, 60J65

Retrieve articles in all journals with MSC: 81P20, 60J65

Additional Information

PII: S 0002-9947(1990)0986033-3
Keywords: Stochastic mechanics, spin diffusions, Bopp-Haag, Dankel, Pauli equation
Article copyright: © Copyright 1990 American Mathematical Society

Comments: Email Webmaster

© Copyright , American Mathematical Society
Contact Us · Sitemap · Privacy Statement

Connect with us Facebook Twitter Google+ LinkedIn Instagram RSS feeds Blogs YouTube Podcasts Wikipedia