Symmetry of the Schr\"odinger equation with variable potential
Mathematical Physics
2015-06-26 v1 math.MP
Abstract
We study symmetry properties of the Schr\"odinger equation with the potential as a new dependent variable, i.e., the transformations which do not change the form of the class of equations. We also consider systems of the Schr\"odinger equations with certain conditions on the potential. In addition we investigate symmetry properties of the equation with convection term. The contact transformations of the Schr\"odinger equation with potential are obtained.
Cite
@article{arxiv.math-ph/9801201,
title = {Symmetry of the Schr\"odinger equation with variable potential},
author = {Wilhelm Fushchych and Zoya Symenoh and Ivan Tsyfra},
journal= {arXiv preprint arXiv:math-ph/9801201},
year = {2015}
}