We prove a criterion for absence of eigenvalues for one-dimensional Schrr odinger operators. This criterion can be regarded as an L 1-version of Gor-don's theorem and it has a broader range of application. Absence of eigenvalues is then established for quasiperiodic potentials generated by Liouville frequencies and various types of functions such as step functions, HH older continuous functions...

In this work, we investigate numerical evolution of massive Kaluza-Klein (KK) modes a scalar field in thick brane. We derive the Klein-Gordon equation five dimensional spacetime, and obtain Schr\"odinger-like equation. With resonances KK as initial data, is evolved with maximally dissipative boundary condition. The results show that there are resonant particles long life on brane, which indicat...

In this work, we investigate the quasinormal modes of a thick brane system. Considering transverse-traceless tensor perturbation metric, obtain Schr\"odinger-like equation Kaluza-Klein perturbation. Then use Wentzel-Kramers-Brillouin approximation and asymptotic iteration method to solve equation. We also study numeric evolution an initial wave packet against brane. The results show that there ...

We use the "tridiagonal representation approach" to solve time-independent Schr\"odinger equation for bound states of generalized versions trigonometric and hyperbolic P\"oschl-Teller potentials. These new solvable potentials do not belong conventional class exactly problems. The solutions are finite series square integrable functions written in terms Jacobi polynomial.

In this review we discuss quantum phase transitions and the mapping between symmetry breaking of electronic structure con® gurations at the large-dimension limit and mean-® eld theory of phase transitions. We show that the ® nite size scaling method can be used for the calculations of the critical parameters of the few-body Schr È odinger equation. In this approach, the ® nite size corresponds ...

Tuncay Aktosun Department of Mathematics North Dakota State University Fargo, ND 58105 Martin Klaus Department of Mathematics Virginia Polytechnic Institute and State University Blacksburg, VA 24061 Cornelis van der Mee Department of Mathematics University of Cagliari Cagliari, Italy Abstract: In this review paper, the generalized Schr odinger equation d2 =dx2 + k2 = [ikP (x) +Q(x)] is conside...

In this paper, we present the main issues and the modelling approaches for the simulation of nanoscale MOSFETs in which transport is dominated by ballistic electrons. We show that is indeed possible to compute in an accurate way the density of states in the channel in the case of quantum confinement without solving the complete two-dimensional Schr€ odinger equation. We are developing modelling...

In this working paper we suggest some lines of investigation regarding oscillatory Fourier transforms with homogeneous phase. A special case is the solution to the time-dependent free Schrr odinger equation. We consider time-global range-weighted L 2 ? R n+1-estimates. The main tools are Parseval's formula for Fourier transforms on R, orthogonality arguments arising from decomposing L 2 (R n) u...

A many-body wave function can be factorized in Fock space into a marginal amplitude describing set of strongly correlated orbitals and conditional for the remaining weakly part. The is solution Schr\"odinger equation with an effective Hamiltonian that viewed as embedding environment electrons. Here, complementary replaced by generalized Kohn-Sham equation, which orbital-dependent functional app...

Excitons in InGaN quantum wells are investigated numerically, considering random alloy disorder and Coulomb interaction on equal footing the Schr\"odinger equation. Their statistical properties systemically explored as a function of well thickness composition, revealing complex competition between disorder-induced carrier localization, attraction, field-induced wave separation. This results cla...