Non-Self-Adjoint Inverse Spectral Theoretic Derivation of a Complex von Neumann-Wigner Potential

摘要

The von Neumann-Wigner potential is a Schroedinger equation potential which supports a positive energy point eigenvalue. The Kay-Moses form of the Gel'fand-Levitan (G-L) equation of inverse spectral theory is used to provide an exact expression, as the published forms leave an unknown function g(r). A non-self-adjoint generalizaion of the G-L equation by the author and H.E. Moses is used to derive a complex generalization of this potential. Exact expressions are given for this potential, the discrete resonant eigenfunction, and the eigenfunctions of the continuous spectrum. A clarifying comment on some non-L sub 2 pseudo-functions used to calculate (all) reflectionless potentials are given. (ERA citation 08:028490)