New situation in quantum mechanics (wonderful potentials from the inverse problem)

Every physicist interested in nonrelativistic wave mechanics can now gain a deeper insight into quantum intuition. This is possible thanks to the advance in the theories of the inverse problem and supersymmetry which provides numerous new classes of exactly solvable models and instructive and clear illustrations revealing the fundamental elements of the coupling between potentials and observables; how to change the disposition of bound states on the energy scale (to shift, create or destroy the spectral levels) and in space by a special choice of potential perturbation. This theory explains the algorithms to control scattering features and wave motion over the lattices (e.g. crystal or discrete variable numbering channels). The best of thousands of corresponding `quantum pictures' are selected here. The predictive power of the acquired intuition allows us to go beyond the scope of the exact models used for its elaboration.