Related papers: Convergent Iterative Solutions of Schroedinger Equ…
We discuss the solutions of the Schroedinger equation for piecewise potentials, given by the harmonic oscillator potential for $\vert x\vert >a$ and an arbitrary function for $\vert x\vert <a$, using elementary methods. The study of this…
Let P be the operator $-\Delta+V$ on R^d, where $V$ is a real potential with several inverse square singularities. The usual non-trapping type high-frequency inequality on the truncated resolvent of $P$ is shown, using semi-classical…
We obtain eigenvalues and eigenfunctions of the Schr\"{o}dinger equation with a hyperbolic double-well potential. We consider exact polynomial solutions for some particular values of the potential-strength parameter and also numerical…
The aim of this paper is to investigate the minimization problem related to a Ginzburg-Landau energy functional, where in particular a nonlinear diffusion of mean curvature-type is considered, together with a classical double well…
The initial value problem for the $L^{2}$ critical semilinear Schr\"odinger equation with periodic boundary data is considered. We show that the problem is globally well posed in $H^{s}({\Bbb T^{d}})$, for $s>4/9$ and $s>2/3$ in 1D and 2D…
The generalized equation for the study of two-component nonlinear waves in different fields of physics is considered. In special cases, this equation is reduced to a set of the various well-known equations describing nonlinear solitary…
The effective mass one-dimensional Schr\"odinger equation for the generalized Morse potential is solved by using Nikiforov-Uvarov method. Energy eigenvalues and corresponding eigenfunctions are computed analytically. The results are also…
The Schr\"odinger equation with a Lennard-Jones potential is solved by using a procedure that treats in a rigorous way the irregular singularities at the origin and at infinity. Global solutions are obtained thanks to the computation of the…
We look for ground state solutions to the Schr\"odinger-type system \[ \begin{cases} -\Delta u_j + \lambda_j u_j = \partial_jF(u)\\ \int_{\rn} u_j^2 \, dx = a_j^2\\ (\lambda_j,u_j) \in \mathbb{R} \times H^1(\mathbb{R}^N) \end{cases} j \in…
We study the existence of solutions of the following nonlinear Schr\"odinger equation $$ -\Delta u+V(x)u-\frac{(N-2)^2}{4|x|^2}u=f(x,u) $$ where $V:\mathbb{R}^N\to\mathbb{R}$ and $f:\mathbb{R}^N\times \mathbb{R}\to \mathbb{R}$ are periodic…
Here we have studied first and second-order intertwining approach to generate isospectral partner potentials of position-dependent (effective) mass Schroedinger equation. The second-order intertwiner is constructed directly by taking it as…
We present a mathematically rigorous quantum-mechanical treatment of a one-dimensional nonrelativistic motion of a particle in the potential field $V(x)=g_{1}x^{-1}+g_{2}x^{-2}$. For $g_{2}>0$ and $g_{1}<0$, the potential is known as the…
We study the following Schr\"odinger-Poisson system (P_\lambda)\{ll} -\Delta u + (1+\mu g(x))u+\lambda \phi (x) u =|u|^{p-1}u, x\in \mathbb{R}^3,
S-state Bound state solution to Schroedinger equation for an exponential potential is derived using the Mellin transform. This method is a new and an alternative to the usual method of reducing Schroedinegr equation to a Bessel differential…
Highly accurate closed-form approximations are given for the ground state and first excited state wavefunctions and energies for a nonrelativistic particle in a one-dimensional double square well potential with a square barrier in between…
Study the following two-component elliptic system% \begin{equation*} \left\{\aligned&\Delta u-(\lambda a(x)+a_0)u+u^3+\beta v^2u=0\quad&\text{in }\bbr^4,\\% &\Delta v-(\lambda b(x)+b_0)v+v^3+\beta u^2v=0\quad&\text{in }\bbr^4,\\%…
In this paper we consider a class of logarithmic Schr\"{o}dinger equations with a potential which may change sign. When the potential is coercive, we obtain infinitely many solutions by adapting some arguments of the Fountain theorem, and…
The generalized Moutard transformation of the stationary axially symmetric Schr\"odinger equation is considered. It is shown that a superposition of two Moutard transformations can provide new potentials for the eigenvalue problem. Examples…
In this paper, the conformable Schrodinger equation for hydrogen atom with given conformable potential is solved. The conformable wave functions and energy levels are obtained, and the traditional energy levels and wave function for…
In a first part of this paper we investigate the continuity (stability) of the spectrum of a class of non-local Schr\"odinger operators on varying the potentials. By imposing conditions of different strength on the convergence of the…