Volume 19, Issue 3, September 2012, Pages 292 - 299
Conservation Laws for the Schrödinger–Newton Equations
Authors
G. Gubbiotti, M. C. Nucci*
Dipartimento di Matematica e Informatica, Università di Perugia & INFN Sezione Perugia, 06123 Perugia, Italy
Received 16 April 2012, Accepted 26 June 2012, Available Online 20 September 2012.
- DOI
- 10.1142/S1402925112200021How to use a DOI?
- Keywords
- Schrödinger–Newton equations; calculus of variations; Noether's theorem
- Abstract
In this Letter a first-order Lagrangian for the Schrödinger–Newton equations is derived by modifying a second-order Lagrangian proposed by Christian [Exactly soluble sector of quantum gravity, Phys. Rev. D 56(8) (1997) 4844–4877]. Then Noether's theorem is applied to the Lie point symmetries determined by Robertshaw and Tod [Lie point symmetries and an approximate solution for the Schrödinger–Newton equations, Nonlinearity 19(7) (2006) 1507–1514] in order to find conservation laws of the Schrödinger–Newton equations.
- Copyright
- © 2012 The Authors. Published by Atlantis Press and Taylor & Francis
- Open Access
- This is an open access article distributed under the CC BY-NC 4.0 license (http://creativecommons.org/licenses/by-nc/4.0/).
Cite this article
TY - JOUR AU - G. Gubbiotti AU - M. C. Nucci PY - 2012 DA - 2012/09/20 TI - Conservation Laws for the Schrödinger–Newton Equations JO - Journal of Nonlinear Mathematical Physics SP - 292 EP - 299 VL - 19 IS - 3 SN - 1776-0852 UR - https://doi.org/10.1142/S1402925112200021 DO - 10.1142/S1402925112200021 ID - Gubbiotti2012 ER -