Odinger-type Equations in One Space Variable

Orthogonal Spline Collocation Methods for Schrr Odinger-type Equations in One Space Variable

We examine the use of orthogonal spline collocation for the semi-discretization of the cubic Schrr odinger equation and the two-dimensional parabolic equation of Tappert. In each case, an optimal order L 2 estimate of the error in the semidiscrete approximation is derived. For the cubic Schrr odinger equation, we present the results of numerical experiments in which the integration in time is p...

Theory of Hybrid Fractional Differential Equations with Complex Order

We develop the theory of hybrid fractional differential equations with the complex order $thetain mathbb{C}$, $theta=m+ialpha$, $0<mleq 1$, $alphain mathbb{R}$, in Caputo sense. Using Dhage's type fixed point theorem for the product of abstract nonlinear operators in Banach algebra; one of the operators is $mathfrak{D}$- Lipschitzian and the other one is completely continuous, we prove the exis...

A Local Strong form Meshless Method for Solving 2D time-Dependent Schrödinger Equations

This paper deals with the numerical solutions of the 2D time dependent Schr¨odinger equations by using a local strong form meshless method. The time variable is discretized by a finite difference scheme. Then, in the resultant elliptic type PDEs, special variable is discretized with a local radial basis function (RBF) methods for which the PDE operator is also imposed in the local matrices. Des...

On Bound States for Systems of Weakly Coupled Schr Odinger Equations in One Space Dimension

Institute for Mathematical Physics on Separation of Variables in the Schrr Odinger Equation for a Particle Interacting with External Field on Separation of Variables in the Schrr Odinger Equation for a Particle Interacting with External Eld

We obtain the most general form of the vector-potential of the electromagnetic eld A enabling separation of variables in the (1+2)-dimensional Schrr odinger equation (SE). Using this result we have carried out variable separation for a class of Schrr odinger equations that contains as particular cases SE with Coulomb scalar potential and SE for a particle interacting with the constant magnetic ...