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

This paper presents a direct potential surface inversion algorithm for mult idimensional quantum systems based on combining probability density and ene rgy spectral data. The algorithm expresses the potential explicitly in term s of the eigenstate probability density and the associated eigenenergies. S imulations show that the inversion can produce excellent results in the reg ular domain away from the asymptotic unidentifiable regions. The regular in vertible domain of the potential can be adjusted by utilizing suitable spec tral data. The inversion algorithm is successfully simulated to extract the potential surfaces of several one- and two-dimensional model systems.