Abstract
The inverse scattering transformation (IST) with the angular momentum (λ) as a spectral variable turned out to be a useful method to deal with rotationally invariant problems in field theory at higher spatial dimensions [Refs. (1) and (2)]. We derive the direct and inverse scattering problems for thev-dimensional radial Schrodinger equation for variable λ and fixed energy (negative or positive). We determine the scattering data (SD) in one to one correspondence with the potential and derive the corresponding Gelfand-Levitan equation. A family of exactly solvable potentials for any λ and fixed energy is obtained. The trace identities associated to this IST are derived for both signs of the energy. They relate integrals of local polynomials in the potential and its derivatives timesr2n−1(n≧1) with the SD. The presence of this power ofr makes these relations useful in higher dimensions.
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