Lie symmetry analysis is an established method for generating symmetries of differential equations. We apply this together the generalized fundamental theorem double reduction. In particular, Noether and some associated conservation laws are constructed in our investigation to find exact solutions higher order partial equations complex

We present a simple method to compute the transmission coefficient of a quantum system embedded between two conducting electrodes. Starting from the solution of the time-dependent Schrodinger equation, we demonstrate the relationship between the temporal evolution of the state vector, |ψ(t)>, initially localized on one electrode and the electronic transmission coefficient, T(E). We particularly...

It is shown that under very general conditions there is a rigorous identity between the group velocity and the velocity of energy transport in nonhomogeneous media with or without anomalous dispersion. The medium is assumed nondissipative and the parameters such as density, rigidity, dielectric constant, etc., vary from point to point but are independent of the Cartesian coordinate lying in the...

in this paper, the numerical solution methods of one- particale, one – dimensional time- independentschrodinger equation are presented that allows one to obtain accurate bound state eigen values andeigen functions for an arbitrary potential energy function v(x). these methods included the fem(finite element method), cooly, numerov and others. here we considered the numerov method inmore details...

We prove the scattering for a defocusing nonlinear Schrodinger equation with sum of two repulsive potentials strictly convex level surfaces, thus providing result in trapped setting similar to exterior obstacles.

We investigate the approximate l-state solutions of Schrödinger equation for Hulthén plus a class Yukawa potential. In this context, we construct bound-state energy and wavefunction expressed by Gauss hypergeometric function means asymptotic iteration approach in detail.

The solution of one-dimensional Schrodinger equation for a newly proposed potential called modified shifted Deng-Fan momentum-dependent is obtained via supersymmetric approach. expectation values momentum and position were calculated using Hellmann Feynman Theorem. effects parameter on the solutions system as well studied. Finally, special cases interacting obtained.