Analytic solutions of the Schrödinger equation with non-central generalized inverse quadratic Yukawa potential

Solitonlike solutions of the generalized discrete nonlinear Schrödinger equation.

ṕ Estimates for the Schrödinger Equation on the Line and Inverse Scattering for the Nonlinear Schrödinger Equation with a Potential ∗

In this paper I prove a L − L estimate for the solutions of the one–dimensional Schrödinger equation with a potential in Lγ where in the generic case γ > 3/2 and in the exceptional case (i.e. when there is a half–bound state of zero energy) γ > 5/2. I use this estimate to construct the scattering operator for the nonlinear Schrödinger equation with a potential. I prove moreover, that the low–en...

Analytical Soliton Solutions Modeling of Nonlinear Schrödinger Equation with the Dual Power Law Nonlinearity  

Introduction In this study, we use a newly proposed method based on the software structure of the maple, called the Khaters method, and will be introducing exponential, hyperbolic, and trigonometric solutions for one of the Schrödinger equations, called the nonlinear Schrödinger equation with the dual power law nonlinearity. Given the widespread use of the Schrödinger equation in physics and e...

Inverse Scattering for the Nonlinear Schrödinger Equation with the Yukawa Potential

We study the inverse scattering problem for the three dimensional nonlinear Schrödinger equation with the Yukawa potential. The nonlinearity of the equation is nonlocal. We reconstruct the potential and the nonlinearity by the knowledge of the scattering states. Our result is applicable to reconstructing the nonlinearity of the semi-relativistic Hartree equation.

Schrödinger equation of general potential

It is well known that the Schrödinger equation is only suitable for the particle in common potential V (~r, t). In this paper, a general Quantum Mechanics is proposed, where the Lagrangian is the general form. The new quantum wave equation can describe the particle which is in general potential V (~r, ~̇r, t). We think these new quantum wave equations can be applied in many fields. PACS numbers:...