DARBOUX TRANSFORMATION OF THE SCHRODINGER-EQUATION

The recent developments in the theory of the generation of potentials for which the Schrodinger equation has an exact solution are discussed , The generalization of the Darboux transformation to the nonstationar y Schrodinger equation is studied in detail. The supersymmetric genera lization of the nonstationary Schrodinger equation is formulated, Vers ions corresponding to exact and spontaneously broken supersymmetry are discussed. New, exactly solvable nonstationary potentials are obtaine d as examples. The stationary Darboux transformation is viewed as a sp ecial case of the new transformation. Families of isospectral potentia ls with the spectra of the harmonic oscillator and the hydrogen-like a tom are obtained. The effectiveness of these methods for describing th e coherent states of the transformed Hamiltonians is demonstrated. (C) 1997 American Institute of Physics.