Symmetry of the Schr\"odinger equation with variable potential

@inproceedings{Fushchych1998SymmetryOT,
  title={Symmetry of the Schr\"odinger equation with variable potential},
  author={Wilhelm I. Fushchych and Z. I. Symenoh and Ivan Tsyfra},
  year={1998}
}
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. 
4 Citations
Differential Invariants, Hidden and Conditional Symmetry
We present a survey of development of the concept of hidden symmetry in the field of partial differential equations, including a series of results previously obtained by the author. We also add new
Symmetry and Solution of Neutron Transport Equations in Nonhomogeneous Media
We propose the group-theoretical approach which enables one to generate solutions of equations of mathematical physics in nonhomogeneous media from solutions of the same problem in a homogeneous
Variable coefficient nonlinear systems derived from an atmospheric dynamical system
Variable coefficient nonlinear systems, the Korteweg de Vries (KdV), the modified KdV (mKdV) and the nonlinear Schrodinger (NLS) type equations, are derived from the nonlinear inviscid barotropic
Диференціальні інваріанти, прихована та умовна симетрія
УДК 517.958:512.86 Наведено огляд розвитку поняття прихованої симетрiї диференцiальних рiвнянь з частинними похiдними та результатiв, отриманих автором ранiше, а також новi приклади класiв рiвнянь,