A representation formula related to Schrodinger operators

Let H be a Schrodinger operator on the real line, where the potential is in L^1 and L^2. We define the perturbed Fourier transform F for H and show that F is an isometry from the absolute continuous subspace onto L^2. This property allows us to construct a kernel formula for spectral operators. The main theorem improves the author's previous result for certain short-range potentials.