Multidimensional potential surfaces from the direct inversion of probability density and energy spectral data

This paper presents a direct potential surface inversion algorithm for multidimensional quantum systems based on combining probability density and energy spectral data. The algorithm expresses the potential explicitly in terms of the eigenstate probability density and the associated eigenenergies. Simulations show that the inversion can produce excellent results in the regular domain away from the asymptotic unidentifiable regions. The regular invertible domain of the potential can be adjusted by utilizing suitable spectral data. The inversion algorithm is successfully simulated to extract the potential surfaces of several one- and two-dimensional model systems.