Skip to main content

Some recent applications of stochastic processes in quantum mechanics

  • Conference paper
  • First Online:
  • 722 Accesses

Part of the book series: Lecture Notes in Mathematics ((LNMCIME,volume 1159))

This is a preview of subscription content, log in via an institution.

Buying options

Chapter
USD   29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD   34.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD   46.00
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Learn about institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. E. Nelson: "Derivation of the Schrödinger Equation from Newtonian Mechanics", Phys. Rev. 150, 1079 (1966); "Dynamical Theories of Brownian Motion", Princeton University Press 1967; "Quantum Fluctuations" Princeton University Press 1984.

    Article  ADS  Google Scholar 

  2. B. Simon: "Functional Integration and Quantum Physics", Acad. Press, New York 1979.

    MATH  Google Scholar 

  3. Here we follow the presentation in G.F.De Angelis, G.Jona-Lasinio: "A Stochastic Description of a Spin — 1/2 Particle in a Magnetic Field", J. Phys. A. 15, 2053 (1982).

    Google Scholar 

  4. S. Albeverio, R. Høegh-Krohn, L. Streit: "Energy Forms, Hamiltonian and Distorted Brownian Paths", J. Math. Phys. 18, 907 (1977).

    Article  ADS  MATH  Google Scholar 

  5. G. Jona-Lasinio, F. Martinelli, E. Scoppola: "New Approach to the Semiclassical Limit of Quantum Mechanics", Comm. Math. Phys. 80, 223 (1981); "The Semiclassical Limit of Quantum Mechanics: A Qualitative Theory via Stochastic Mechanics", Phys. Rep. 77, 313 (1981).

    Article  ADS  MATH  MathSciNet  Google Scholar 

  6. S. Graffi, V. Grecchi, G. Jona-Lasinio: "Tunnelling Instability via Perturbation Theory", J. Phys. A. 17, 2935 (1984).

    Article  ADS  MATH  MathSciNet  Google Scholar 

  7. B.Helffer, J.Sjöstrand: "Puits Multiples en Limite Semi-Classique" Preprint 1984.

    Google Scholar 

  8. B.Simon: "Semiclassical Analysis of Low Lying Eigenvalues, IV the Flea on the Elephant", Preprint 1984.

    Google Scholar 

  9. G.Jona-Lasinio, F.Martinelli, E.Scoppola: "Multiple Tunnellings in d-Dimensions: A Quantum Particle in a Hierarchical Potential", to appear in Annales de l'Institut Henri Poincaré.

    Google Scholar 

  10. P.Claverie, G.Jona-Lasinio: "Instability of Tunneling and the Concept of Molecular Structure in Quantum Mechanics: Some Remarks on the Enantiomer Problem", Preprint 1984.

    Google Scholar 

  11. G. Jona-Lasinio, F. Martinelli, E. Scoppola: "Decaying Quantum Mechanical States: An Informal Discussion within Stochastic Mechanics", Lett. Nuovo Cimento 34, 13 (1982).

    Article  MathSciNet  Google Scholar 

  12. A.D.Ventzel, M.I. Freidlin: "Dynamical Systems under the Action of Small Random Perturbations", Springer 1983.

    Google Scholar 

  13. G.F. De Angelis, G. Jona-Lasinio, M. Sirugue: "Probabilistic Solution of Pauli Type Equations", J. Phys. A 16, 2433 (1983).

    Article  ADS  MATH  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 1985 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Jona-Lasinio, G. (1985). Some recent applications of stochastic processes in quantum mechanics. In: Graffi, S. (eds) Schrödinger Operators. Lecture Notes in Mathematics, vol 1159. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0080335

Download citation

  • DOI: https://doi.org/10.1007/BFb0080335

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-16035-9

  • Online ISBN: 978-3-540-39706-9

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics