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We examine the bound state and scattering problem of a spin-one-half particle undergone to an Aharonov-Bohm potential in a conical space in the nonrelativistic limit. The crucial problem of the \delta-function singularity coming from the…

Quantum Physics · Physics 2012-02-24 F. M. Andrade , E. O. Silva , M. Pereira

Non-self-adjoint Schrodinger operators which correspond to non-symmetric zero-range potentials are investigated. We show that various properties of these operators (eigenvalues, exceptional points, spectral singularities and the property of…

Mathematical Physics · Physics 2015-06-19 P. A. Cojuhari , A. Grod , S. Kuzhel

We examine two kinds of spectral theoretic situations: First, we recall the case of self-adjoint half-line Schr\"odinger operators on $[a,\infty)$, $a\in\mathbb{R}$, with a regular finite end point $a$ and the case of Schr\"odinger…

Spectral Theory · Mathematics 2020-02-25 Fritz Gesztesy , Maxim Zinchenko

We study the relativistic version of Schr\"odinger equation for a point particle in 1-d with potential of the first derivative of the delta function. The momentum cutoff regularization is used to study the bound state and scattering states.…

High Energy Physics - Theory · Physics 2015-08-05 M. H. Al-Hashimi , A. M. Shalaby

The matrix Schroedinger equation with a selfadjoint matrix potential is considered on the half line with the most general selfadjoint boundary condition at the origin. When the matrix potential is integrable and has a first moment, it is…

Mathematical Physics · Physics 2015-05-28 Tuncay Aktosun , Martin Klaus , Ricardo Weder

We extend the notion of Dirac oscillator in two dimensions, to construct a set of potentials. These potentials becomes exactly and quasi-exactly solvable potentials of non-relativistic quantum mechanics when they are transformed into a…

Quantum Physics · Physics 2009-11-11 Ramazan Koc , Mehmet Koca

We give necessary and sufficient conditions for real sequences to be the spectra of selfadjoint extensions of an entire operator whose domain may be non-dense. For this spectral characterization we use de Branges space techniques and a…

Mathematical Physics · Physics 2012-10-23 Luis O. Silva , Julio H. Toloza

Making an ansatz to the wave function, the exact solutions of the $D$% -dimensional radial Schrodinger equation with some molecular potentials like pseudoharmonic and modified Kratzer potentials are obtained. The restriction on the…

Quantum Physics · Physics 2009-11-13 Sameer M. Ikhdair , Ramazan Sever

We study the radial Schroedinger equation for a particle in the field of a singular inverse square attractive potential. This potential is relevant to the fabrication of nanoscale atom optical devices, is said to be the potential describing…

Quantum Physics · Physics 2008-11-26 M. Bawin , S. A. Coon

In the paper, in the scattering problem for the valence electron model potential a self-adjoint extension is performed and Rutherford formula is modified. The scattering of slow particles for this potential is also discussed and the changes…

General Physics · Physics 2025-03-24 Anzor Khelashvili , Teimuraz Nadareishvili

We develop a general technique for finding self-adjoint extensions of a symmetric operator that respect a given set of its symmetries. Problems of this type naturally arise when considering two- and three-dimensional Schr\"odinger operators…

Mathematical Physics · Physics 2010-12-14 D. M. Gitman , A. G. Smirnov , I. V. Tyutin , B. L. Voronov

The transmission eigenvalues corresponding to the half-line Schr\"odinger equation with the general selfadjoint boundary condition is analyzed when the potential is real valued, integrable, and compactly supported. It is shown that a…

Spectral Theory · Mathematics 2016-10-06 Tuncay Aktosun , Vassilis G. Papanicolaou

We study the spectral properties of a Schr\"odinger operator, in presence of a confining potential given by the distance squared from a fixed compact potential well. We prove continuity estimates on both the eigenvalues and the eigenstates,…

Analysis of PDEs · Mathematics 2025-05-19 Chiara Alessi , Lorenzo Brasco , Michele Miranda

The purpose of this paper is to study spectral properties of non-self-adjoint Schr\"odinger operators $-\Delta-\frac{(n-2)^2}{4|x|^{2}}+V$ on $\mathbb{R}^n$ with complex-valued potentials $V\in L^{p,\infty}$, $p>n/2$. We prove Keller type…

Spectral Theory · Mathematics 2016-08-08 Haruya Mizutani

We apply the Asymptotic Iteration Method to obtain the bound-state energy spectrum for the d-dimensional Klein-Gordon equation with scalar S(r) and vector potentials V(r). When S(r) and V(r) are both Coulombic, we obtain all the exact…

Mathematical Physics · Physics 2009-11-13 Nasser Saad , Richard L. Hall , Hakan Ciftci

In this paper we construct the spectral expansion for the non-self-adjoint differential operators generated in the space of vektor functions by the ordinary differential expression of arbitrary order with the periodic matrix coefficients by…

Spectral Theory · Mathematics 2021-12-24 O. A. Veliev

In this work the bound state and scattering problems for a spin-1/2 particle undergone to an Aharonov-Bohm potential in a conical space in the nonrelativistic limit are considered. The presence of a \delta-function singularity, which comes…

Quantum Physics · Physics 2013-10-25 F. M. Andrade , E. O. Silva , M. Pereira

We discuss magnetic Schrodinger operators perturbed by measures from the generalized Kato class. Using an explicit Krein-like formula for their resolvent, we prove that these operators can be approximated in the strong resolvent sense by…

Mathematical Physics · Physics 2007-05-23 Katerina Ozanova

In our previous work, we introduced the concept of a \emph{spectral pair} for a half-line Schr\"odinger operator with a \emph{complex} bounded potential $q$, serving as a substitute for the spectral measure in a non-self-adjoint setting. In…

Spectral Theory · Mathematics 2026-01-09 Alexander Pushnitski , František Štampach

The spectrum of r-1 and r-2 type potentials of diatomic molecules in radial Schrodinger equation are calculated by using the formalism of asymptotic iteration method. The alternative method is used to solve eigenvalues and eigenfunctions of…

Mathematical Physics · Physics 2016-11-26 Ozgur Oztemel , Eser Olgar