In this paper we study eigenfunction expansions associated with the Schrodinger operator with a singular potential. In the paper it is obtained sufficient conditions for localization and uniformly convergence of the regularizations of the corresponding expansions

For |Ψ an eigenfunction of the Hamiltonian operatorˆH = ˆ T + ˆ V , wherê T is the kinetic energy operator andˆV the potential energy operator , the following relations between expectation values are satisfied:

The asymptotic behaviour of a finite energy pseudoholomorphic strip with Lagrangian boundary conditions in a symplectic manifold is determined by an eigenfunction of the linearized operator at the (transverse) intersection.

A general Casoratian formulation is proposed for the 2D Toda lattice equation, which involves coupled eigenfunction systems. Various Casoratian type solutions are generated, through solving the resulting linear conditions and using a Bäcklund transformation.

In the present paper, we study properties of second Dirichlet eigenvalue fractional Laplacian annuli-like domains and corresponding eigenfunctions. first part, consider an annulus with inner radius $ R outer R+1 $. We show that for sufficiently large any eigenfunction this is nonradial. investigate in form B_1(0)\setminus \overline{B_{\tau}(a)} $, where a unitary ball 0<\tau<1-|a| value m...

DAI, Z.-J.; CHEN, J.-Y.; DU, J.-Z., and LI, C.-C., 2008. Seasonal changes of sandbar behavior in Nanwan Beach, South China. Journal of Coastal Research, 24(5), 1209–1216. West Palm Beach (Florida), ISSN 0749-0208. Frequent leveling data of beach profiles is collected from Nanwan Beach, which is characterized by a large seasonal variation in wave climate. Variability of the bar crest position ob...

We study many-body properties of quantum harmonic oscillator lattices with disorder. A sufficient condition for dynamical localization, expressed as a zero-velocity LiebRobinson bound, is formulated in terms of the decay of the eigenfunction correlators for an effective one-particle Hamiltonian. We show how state-of-the-art techniques for proving Anderson localization can be used to prove that ...