Dispersion for the Schrödinger Equation on the Line with Multiple Dirac Delta Potentials and on Delta Trees
نویسندگان
چکیده
Abstract. In this paper we consider the time dependent one-dimensional Schrödinger equation with multiple Dirac delta potentials of different positive strengths. We prove that the classical dispersion property holds. The result is obtained in a more general setting of a Laplace operator on a tree with δ-coupling conditions at the vertices. The proof relies on a careful analysis of the properties of the resolvent of the associated Hamiltonian. With respect to the analysis done for Kirchoff conditions, here the resolvent is no longer in the framework of Wiener algebra of almost periodic functions, and its expression is harder to analyze.
منابع مشابه
Wave Operator Bounds for 1-dimensional Schrödinger Operators with Singular Potentials and Applications
Boundedness of wave operators for Schrödinger operators in one space dimension for a class of singular potentials, admitting finitely many Dirac delta distributions, is proved. Applications are presented to, for example, dispersive estimates and commutator bounds.
متن کاملVibration Suppression of Simply Supported Beam under a Moving Mass using On-Line Neural Network Controller
In this paper, model reference neural network structure is used as a controller for vibration suppression of the Euler–Bernoulli beam under the excitation of moving mass travelling along a vibrating path. The non-dimensional equation of motion the beam acted upon by a moving mass is achieved. A Dirac-delta function is used to describe the position of the moving mass along the beam and its iner...
متن کاملMapping of Agricultural Information Flows for Yam Minisett Technology in Delta State, Nigeria
ABSTRACTThis study examined information flow on minisett technology among yam farmers in Delta State, Nigeria. A sample size of 180 respondents was involved in the study. Data were obtained from respondents of the study through the use of a validated interview schedule. Percentage, frequency count and mean scores were used to summarize data, while line diagrams were used to develop maps of info...
متن کاملOn relation between the Kirchhoff index and number of spanning trees of graph
Let $G=(V,E)$, $V={1,2,ldots,n}$, $E={e_1,e_2,ldots,e_m}$,be a simple connected graph, with sequence of vertex degrees$Delta =d_1geq d_2geqcdotsgeq d_n=delta >0$ and Laplacian eigenvalues$mu_1geq mu_2geqcdotsgeqmu_{n-1}>mu_n=0$. Denote by $Kf(G)=nsum_{i=1}^{n-1}frac{1}{mu_i}$ and $t=t(G)=frac 1n prod_{i=1}^{n-1} mu_i$ the Kirchhoff index and number of spanning tree...
متن کاملCharacterization of $(delta, varepsilon)$-double derivation on rings and algebras
This paper is an attempt to prove the following result:Let $n>1$ be an integer and let $mathcal{R}$ be a $n!$-torsion-free ring with the identity element. Suppose that $d, delta, varepsilon$ are additive mappings satisfyingbegin{equation}d(x^n) = sum^{n}_{j=1}x^{n-j}d(x)x^{j-1}+sum^{n-1}_{j=1}sum^{j}_{i=1}x^{n-1-j}Big(delta(x)x^{j-i}varepsilon(x)+varepsilon(x)x^{j-i}delta(x)Big)x^{i-1}quadend{e...
متن کامل