By Oktay Veliev
The e-book describes the direct difficulties and the inverse challenge of the multidimensional Schrödinger operator with a periodic capability. This matters perturbation conception and confident selection of the spectral invariants and discovering the periodic strength from the given Bloch eigenvalues. the original approach to this booklet derives the asymptotic formulation for Bloch eigenvalues and Bloch capabilities for arbitrary size. furthermore, the degree of the iso-energetic surfaces within the excessive strength area is build and envisioned. It implies the validity of the Bethe-Sommerfeld conjecture for arbitrary dimensions and arbitrary lattices. utilizing the perturbation concept built during this e-book, the spectral invariants of the multidimensional operator from the given Bloch eigenvalues are decided. a few of these invariants are explicitly expressed by means of the Fourier coefficients of the aptitude. this manner the prospect to figure out the capability constructively through the use of Bloch eigenvalues as enter information is given. after all an set of rules for the original selection of the aptitude is given.
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