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We obtain lower bounds on the ground state energy, in one and three dimensions, for the spinless Salpeter equation (Schr\"odinger equation with a relativistic kinetic energy operator) applicable to potentials for which the attractive parts…

Mathematical Physics · Physics 2015-06-26 Fabian Brau

In this paper, we consider the scattering problem for a class of $N$-coupled systems of the cubic nonlinear Schr\"odinger equations in three space dimensions. We prove the scattering of solutions that have a mass-energy quantity less than…

Analysis of PDEs · Mathematics 2023-03-23 Satoshi Masaki , Ryusei Tsukuda

The Schrodinger equation for stationary states is studied in a central potential V(r) proportional to the inverse power of r of degree beta in an arbitrary number of spatial dimensions. The presence of a single term in the potential makes…

Quantum Physics · Physics 2007-05-23 Shi-Hai Dong , Zhong-Qi Ma , Giampiero Esposito

In this paper, we propose an iterative method to compute the positive ground states of saturable nonlinear Schr\"odinger equations. A discretization of the saturable nonlinear Schr\"odinger equation leads to a nonlinear algebraic eigenvalue…

Numerical Analysis · Mathematics 2019-07-11 Ching-Sung Liu

In this paper we prove the existence of infinitely many small energy solution of a semilinear Schrodinger equation via the dual form of the generalized fountain theorem. This equation is with periodic potential and concave-convex…

Analysis of PDEs · Mathematics 2014-01-28 Long-Jiang Gu , Hong-Rui Sun

The series solution of the radial part of the Schr\"odinger equation for simultaneous coulomb and harmonic potential involves three-term recursion relation and is thus difficult to solve for bound states. We have suggested a simple method…

Mathematical Physics · Physics 2013-08-12 Jishnu Goswami , Chandan Mondal , Dipankar Chakrabarti

We found a simple procedure for the solution of the time - independent Schrodinger equation in one dimension without making any approximation. The wave functions are always periodic. Two difficulties may be encountered: one is to solve the…

Quantum Physics · Physics 2007-05-23 H. H. Erbil

In the paper the Schr\"odinger equation for quasibound resonance state with complex energy is considered. The system of inhomogeneous differential equations is obtained for the real and imaginary parts of wave function. On the base of known…

Nuclear Theory · Physics 2009-10-31 Il-Tong Cheon , G. Kim , A. V. Khugaev

We present the exact solution of the stationary Schr\"odinger equation equation for the potential $V=V_0/{\sqrt{x}}$. Each of the two fundamental solutions that compose the general solution of the problem is given by a combination with…

Quantum Physics · Physics 2015-10-26 A. M. Ishkhanyan

Using Mathematica 3.0, the Schroedinger equation for bound states is solved. The method of solution is based on a numerical integration procedure together with convexity arguments and the nodal theorem for wave functions. The interaction…

High Energy Physics - Phenomenology · Physics 2015-06-25 Wolfgang Lucha , F. F. Schoberl

In this paper, we look for solutions to the following coupled Schr\"{o}dinger system \begin{equation*} \begin{cases} -\Delta u+\lambda_{1}u=\alpha_{1}|u|^{p-2}u+\mu_{1}u^{3}+\rho v^{2}u & \text{in} \ \ \mathbb{R}^{N}, -\Delta…

Analysis of PDEs · Mathematics 2021-08-26 Maoding Zhen

The general solution of the one-dimensional stationary Schroedinger equation in the form of a formal power series is considered. Its efficiency for numerical analysis of initial value and boundary value problems is discussed.

Mathematical Physics · Physics 2007-09-19 Vladislav V. Kravchenko

We present analytically the exact energy bound-states solutions of the Schrodinger equation in D-dimensions for a recently proposed modified Kratzer potential plus ring-shaped potential by means of the conventional Nikiforov-Uvarov method.…

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

The procedure proposed recently by J.Bougie, A.Gangopadhyaya and J.V.Mallow to study the general form of shape invariant potentials in one-dimensional Supersymmetric Quantum Mechanics (SUSY QM) is generalized to the case of Higher Order…

Quantum Physics · Physics 2015-05-20 F. Cannata , M. V. Ioffe , E. V. Kolevatova , D. N. Nishnianidze

By employing the Pekeris approximation, the D-dimensional Schr\"odinger equation is solved for the nuclear deformed Woods-Saxon potential plus double ring-shaped potential within the framework of the Asymptotic Iteration Method (AIM). The…

Nuclear Theory · Physics 2016-05-30 M. Chabab , A. El Batoul , M. Oulne

The second order $N$-dimensional Schr\"odinger equation with pseudoharmonic potential is reduced to a first order differential equation by using the Laplace transform approach and exact bound state solutions are obtained using convolution…

Mathematical Physics · Physics 2016-01-05 Tapas Das , Altug Arda

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

A slightly modified variant of the cubic periodic one-dimensional nonlinear Schroedinger equation is shown to admit weak solutions for all initial data in certain function spaces wider than L^2. These solutions depend uniformly continuously…

Analysis of PDEs · Mathematics 2007-05-23 Michael Christ

We study the asymptotics of the Schr\"odinger equation with time-dependent potential in dimension one. Assuming that the potential decays sufficiently rapidly as $|x| \to \infty$, we prove that the solution can be written as the sum of a…

Analysis of PDEs · Mathematics 2025-12-30 Gavin Stewart , Avy Soffer

Recently, the Asymptotic Iteration Method (AIM) was used to calculate the energy spectrum for a short rang three parameter central potential which was introduced by H. Bahlouli and A. D. Alhaidari. The S-orbital wave solution of the…

Quantum Physics · Physics 2018-02-14 Abdulla Jameel Sous , M. I. El-Kawni