The Periodic Schr odinger Operators with Potentialsin the C

Propagation Properties for Schr Odinger Operators Affiliated to Certain C*{algebras

We consider anisotropic Schrr odinger operators H = ?+V in L 2 (R n). To certain asymptotic regions F we assign asymptotic Hamiltonians H F such that (a) (H F) ess(H), (b) states with energies not belonging to (H F) do not propagate into a neighbourhood of F under the evolution group deened by H. The proof relies on C*-algebra techniques. We can treat in particular potentials that tend asymptot...

Theory of Hybrid Fractional Differential Equations with Complex Order

We develop the theory of hybrid fractional differential equations with the complex order $thetain mathbb{C}$, $theta=m+ialpha$, $0<mleq 1$, $alphain mathbb{R}$, in Caputo sense. Using Dhage's type fixed point theorem for the product of abstract nonlinear operators in Banach algebra; one of the operators is $mathfrak{D}$- Lipschitzian and the other one is completely continuous, we prove the exis...

Absolute Continuity of the Periodicmagnetic Schr Odinger Operatoralexander

We prove that the spectrum of the Schrr odinger operator with periodic electric and magnetic potentials is absolutely continuous.

Absolute Continuity of Periodic Schr odinger

We consider the Schrr odinger operator ? + V in R d with periodic potential V in the Kato class. We show that, if d = 2 or 3, the spectrum of ?+V is purely absolutely continuous.

Locating the Spectrum for Magnetic Schr Odinger and Dirac Operators