Nonlinear evolution equations associated with the Schrödinger spectral problem

Abstract 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.