Nonlinear evolution equations associated with the Schrodinger spectral problem

Evolution equations associated with the Schrodinger equation are derived for an arbitrary time-dependent potential. It is shown that the eigenvalues evolve according to the Hellmann-Feynman theorem, while the eigenfunction evolution can be determined either by solving a system of coupled differential equations or by a contour integration in the complex k-domain. A possible application to solving a class of Schrodinger spectral problems is also discussed. (C) 2017 Elsevier Ltd. All rights reserved.