相关论文: On eigenfunction approximations for typical non-se…
We prove that the eigenvalues of a certain highly non-self-adjoint operator that arises in fluid mechanics correspond, up to scaling by a positive constant, to those of a self-adjoint operator with compact resolvent; hence there are…
Inequalities are derived for sums and quotients of eigenvalues of magnetic Schroedinger operators with non-negative electric potentials in domains. The bounds reflect the correct order of growth in the semi-classical limit.
We prove an asymptotic expansion for the eigenvalues and eigenfunctions of Schr\"{o}dinger-type operator with a confining potential and with principle part a periodic elliptic operator in divergence form. We compare the spectrum to the…
We extend a result of Stolz and Weidmann on the approximation of isolated eigenvalues of singular Sturm-Liouville and Dirac operators by the eigenvalues of regular operators.
We introduce a relativistic version of the non-self-adjoint operator obtained by a dilation analytic transformation of the quantum harmonic oscillator. While the spectrum is real and discrete, we show that the eigenfunctions do not form a…
This paper is dedicated to the efficient numerical computation of solutions to the 1D stationary Schr\"odinger equation in the highly oscillatory regime. We compute an approximate solution based on the well-known WKB-ansatz, which relies on…
We consider the Schr\"odinger operator with a periodic potential on quasi-1D models of armchair single-wall nanotubes. The spectrum of this operator consists of an absolutely continuous part (intervals separated by gaps) plus an infinite…
Eigenfunctions of the fractional Schr\"odinger operators in a domain $\mathcal{D}$ are considered, and a relation between the supremum of the potential and the distance of a maximizer of the eigenfunction from $\partial\mathcal{D}$ is…
We propose a numerical method for evaluating eigenvalues and eigenfunctions of Schr\"odinger operators with general confining potentials. The method is selective in the sense that only the eigenvalue closest to a chosen input energy is…
We consider semiclassical Schroedinger operators on R^n, with C^\infty potentials decaying polynomially at infinity. The usual theories of resonances do not apply in such a non-analytic framework. Here, under some additional conditions, we…
We consider the limit measures induced by the rescaled eigenfunctions of single-well Schr\"odinger operators. We show that the limit measure is supported on $[-1,1]$ and with the density proportional to $(1-|x|^\beta)^{-1/2}$ when the…
Eigenfunctions of the Schrodinger equation with the Coulomb potential in the imaginary Lobachevsky space are studied in two coordinate systems admitting solutions in terms of hypergeometric functions. Normalization and coefficients of…
This is an expository paper about self-adjoint extensions of the Laplacian on R^d, initially defined on functions supported away from a point. Let L be the Laplacian with domain smooth functions with compact support away from the origin. We…
We study two- and three-dimensional matrix Schr\"odinger operators with $m\in \mathbb N$ point interactions. Using the technique of boundary triplets and the corresponding Weyl functions, we complete and generalize the results obtained by…
This article is devoted to the construction of pseudomodes of one-dimensional biharmonic operators with the complex-valued potentials via the WKB method. As a by-product, the shape of pseudospectrum near infinity can be described. This is a…
We prove that the wave operators for Schr\"odinger operators with multi-center local point interactions are the scaling limits of the ones for Schr\"odinger operators with regular potentials. We simultaneously present a proof of the…
We describe a suite of fast algorithms for evaluating Jacobi polynomials, applying the corresponding discrete Sturm-Liouville eigentransforms and calculating Gauss-Jacobi quadrature rules. Our approach is based on the well-known fact that…
This paper addresses two different but related questions regarding an unbounded symmetric tridiagonal operator: its self-adjointness and the approximation of its spectrum by the eigenvalues of its finite truncations. The sufficient…
We continue the work of [Camano, Lackner, Monk, SIAM J. Math. Anal., Vol. 49, No. 6, pp. 4376-4401 (2017)] on electromagnetic Stekloff eigenvalues. The authors recognized that in general the eigenvalues due not correspond to the spectrum of…
Kernel-based methods in Numerical Analysis have the advantage of yielding optimal recovery processes in the "native" Hilbert space $\calh$ in which they are reproducing. Continuous kernels on compact domains have an expansion into…