Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
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.
B. Simon: "Functional Integration and Quantum Physics", Acad. Press, New York 1979.
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).
S. Albeverio, R. Høegh-Krohn, L. Streit: "Energy Forms, Hamiltonian and Distorted Brownian Paths", J. Math. Phys. 18, 907 (1977).
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).
S. Graffi, V. Grecchi, G. Jona-Lasinio: "Tunnelling Instability via Perturbation Theory", J. Phys. A. 17, 2935 (1984).
B.Helffer, J.Sjöstrand: "Puits Multiples en Limite Semi-Classique" Preprint 1984.
B.Simon: "Semiclassical Analysis of Low Lying Eigenvalues, IV the Flea on the Elephant", Preprint 1984.
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.
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.
G. Jona-Lasinio, F. Martinelli, E. Scoppola: "Decaying Quantum Mechanical States: An Informal Discussion within Stochastic Mechanics", Lett. Nuovo Cimento 34, 13 (1982).
A.D.Ventzel, M.I. Freidlin: "Dynamical Systems under the Action of Small Random Perturbations", Springer 1983.
G.F. De Angelis, G. Jona-Lasinio, M. Sirugue: "Probabilistic Solution of Pauli Type Equations", J. Phys. A 16, 2433 (1983).
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights 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