The harmonic oscillator in anti de Sitter space(AdS) is discussed. We consider the harmonic oscillator potential and then time independent Schrodinger equation in AdS space. Then we apply the supersymmetric Quantum Mechanics approach to solve our differential equation. In this paper we have solved Schrodinger equation for harmonic oscillator in AdS spacetime by supersymmetry approach. The shape...

Introduction. We are going to present here some brief survey of the results of Theory of Solitons (see [1–3]) from the viewpoint of periodic theory including some new results in the theory of 2-dimensional periodic Schrodinger Operators. A remarkable connection of some very special but highly nontrivial nonlinear (especially one-dimensional) systems with spectral properties of one-dimensional l...

A new computational method for determining the eigenvalues and eigenfunctions of the Schrodinger equation is described. Conventional methods for solving this problem rely on diagonalization of a Hamiltonian matrix or iterative numerical solutions of a time independent wave equation. The new method, in contrast, is based on the spectral properties of solutions to the time-dependent Schrodinger e...

We consider the nonlinear Schrodinger equation with the nonlinearity management which describes Bose-Einstein condensates under Feshbach resonance. By using an averaging theory, we derive the Hamiltonian averaged equation and compare it with other averaging methods developed for this problem. The averaged equation is used for analytical approximations of nonlinearity-managed solitons.

Abstract. We consider a nonlinear Schrodinger equation (NLS) with dissipation and forcing in critical dimension. Without both linear and nonlinear dissipation NLS results in a flnite-time singularity (collapse) for any initial conditions. Dissipation ensures collapse regularization. If dissipation is small then multiple near-singular collapses are randomly distributed in space and time forming ...

We have recently presented a method for solving the time-dependent Schrodinger equation by collocation on various members of a family of spatial grids and have shown that this method is interpretable in terms of the expansion of the wave function in a basis of discrete coordinate eigenfunctions. The method is applicable to molecular systems with one or multiple spatial dimensions, and also to b...

Based on unified theory of electromagnetic interactions and gravitational interactions, the non-relativistic limit of the equation of motion of a charged Dirac particle in gravitational field is studied. From the Schrodinger equation obtained from this non-relativistic limit, we could see that the classical Newtonian gravitational potential appears as a part of the potential in the Schrodinger ...

In order to solve nonlinear kinetic equations for recombination reactions when the production of participating species is driven externally at a time-dependent rate, we establish a framework based on the correspondence between these equations and a Schrodinger-type equation in which the product of the recombination constant with the production rate plays the role of the potential. The required ...

A method of connecting the Korteweg~e Vries (KdV) equation, known from the theory of nonlinear waves, with the SchrOdinger equation was discovered in 1967,Pl This method is applied in the present paper to a study of a periodic problem. We find exact analytical formulae for a class of solutions u (x ,t) such that at any moment in time t the potential u (x ,t) of the Schrodinger operator has only...