Abstract
We examine a recently proposed family of nonlinear Schrödinger equations with respect to a group of transformations that linearize a subfamily of them. We investigate the structure of the whole family with respect to the linearizing transformations, and propose a new, invariant parameterization.
This is a preview of subscription content, log in via an institution.
Buying options
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsPreview
Unable to display preview. Download preview PDF.
References
H.-D. Doebner and G. A. Goldin, On a general nonlinear Schrödinger equation admitting diffusion currents, Phys. Lett. A 162: 397 (1992)
H.-D. Doebner and G. A. Goldin, Group theoretical foundations of nonlinear quantum mechanics, in: “Annales de Fisica, Monografias, Vol. II”, p. 442, CIEMAT, Madrid (1993)
H.-D. Doebner and G. A. Goldin, Manifolds, general symmetries, quantization, and nonlinear quantum mechanics, in: “Proceedings of the First German-Polish Symposium on Particles and Fields, Rydzyna Castle, 1992”, p. 115, World Scientific, Singapore (1993)
H.-D. Doebner and G. A. Goldin, Properties of nonlinear Schrödinger equations associated with diffeomorphism group representations, J. Phys. A: Math. Gen. 27: 1771 (1994)
P. Nattermann, “Struktur und Eigenschaften einer Familie nichtlinearer Schrödingergleichungen”, Diplom thesis; Technical University of Clausthal (1993)
P. Nattermann, Solutions of the general Doebner-Goldin equation via nonlinear transformations, in: “Proceedings of the XXVI Symposium on Mathematical Physics, Torun, December 7–10, 1993”, p. 47, Nicolas Copernicus University Press, Torun (1994)
G. Auberson and P. C. Sabatier, On a class of homogemeous nonlinear Schrödinger equations, J. Math. Phys. 35: 4028 (1994)
H.-D. Doebner, G. A. Goldin and P. Nattermann, work in progress, to be submitted for publication.
S. Weinberg, Testing quantum mechanics, Ann. Phys. (NY) 194: 336 (1989)
P. Nattermann, Symmetry, local linearization, and gauge classification of the Doebner-Goldin equation, Clausthal-preprint ASI-TPA/8/95, Rep. Math. Phys. (to appear)
R. P. Feynman and A. R. Hibbs, “Quantum Mechanics and Path Integrals”, McGraw-Hill, New York (1965).
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 1995 Springer Science+Business Media New York
About this chapter
Cite this chapter
Doebner, HD., Goldin, G.A., Nattermann, P. (1995). A Family of Nonlinear Schrödinger Equations: Linearizing Transformations and Resulting Structure. In: Antoine, JP., Ali, S.T., Lisiecki, W., Mladenov, I.M., Odzijewicz, A. (eds) Quantization, Coherent States, and Complex Structures. Springer, Boston, MA. https://doi.org/10.1007/978-1-4899-1060-8_3
Download citation
DOI: https://doi.org/10.1007/978-1-4899-1060-8_3
Publisher Name: Springer, Boston, MA
Print ISBN: 978-1-4899-1062-2
Online ISBN: 978-1-4899-1060-8
eBook Packages: Springer Book Archive