Eur. Phys. J. D 44, 407-410 (2007)
https://doi.org/10.1140/epjd/e2007-00204-8

Conservation laws derived by the Neutral-Action Method

A simple application to the Schrödinger equation

University of Bremen, Department of Production Engineering, P.O. Box 330, IW3-FB4, 28334 Bremen, Germany

Corresponding author: ^a rkienzler@uni-bremen.de

Received: 6 September 2006
Revised: 7 February 2007
Published online: 22 June 2007

Abstract

Conservation laws are a recognized tool in physical- and engineering sciences. The classical procedure to construct conservation laws is to apply Noether's Theorem. It requires the existence of a Lagrange-function for the system under consideration. Two unknown sets of functions have to be found. A broader class of such laws is obtainable, if Noether's Theorem is used together with the Bessel-Hagen extension, raising the number of sets of unknown functions to three. By using the recently developed Neutral-Action Method, the same conservation laws can be obtained by calculating only one unknown set of functions. Moreover the Neutral Action Method can also be applied in the absence of a Lagrangian, since only the governing differential equations are required for this procedure. In the paper, an application of this method to the Schrödinger equation is presented.