Toward the spectral zone control

The desired shifts of the boundaries of spectral allowed zones of periodical systems are demonstrated. In particular, the phenomenon of merging neighbor allowed zones is exhibited and its simple explanation is given. It is also shown how to change the additional fundamental spectral parameter, the degree of exponential solution growth, at arbitrary given energy points inside the forbidden zones. This allows one to control tunneling through fragments of periodic structures at energies belonging to spectral gap. All the results are based on the finite interval inverse eigenvalue problem which provides us with complete sets of exactly solvable models. This is a radical extension (continuous ! multiplicity) in comparison to the famous finite-gap models.