Intertwining relations of non-stationary Schr\"odinger operators

Abstract

General first- and higher-order intertwining relations between non-stationary one-dimensional Schr\"odinger operators are introduced. For the first-order case it is shown that the intertwining relations imply some hidden symmetry which in turn results in a $R$-separation of variables. The Fokker-Planck and diffusion equation are briefly considered. Second-order intertwining operators are also discussed within a general approach. However, due to its complicated structure only particular solutions are given in some detail.