We analyze the generalized time-dependent Schrödinger equation for the force free case, as a generalization, for example, of the standard time-dependent Schrödinger equation, time fractional Schrödinger equation, distributed order time fractional Schrödinger equation, and tempered in time Schrödinger equation. We relate it to the corresponding standard Schrödinger equation with effective potent...

A model for intrinsic decoherence in quantum mechanics is proposed, based on a simple modification of unitary Schrodinger evolution. On sufticiently small time scales the system evolves by a random sequence of unitary phase changes generated by the Hamiltonian. The Schrodinger equation is obtained to zeroth order in the expansion parameter. Higher-order corrections lead to a loss of coherence i...

It is shown that in the complex trajectory representation of quantum mechanics, the Born’s Ψ⋆Ψ probability density can be obtained from the imaginary part of the velocity field of particles on the real axis. Extending this probability axiom to the complex plane, we first attempt to find a probability density by solving an appropriate conservation equation. The characteristic curves of this cons...

we will present a detailed investigation of intersubband transitions process in core-multi shells quantum dots. the confined wave functions and eigenenergies of electrons in quantum dots have been calculated under the effective-mass approximation by solving a three-dimensional schrodinger equation. excellent dependence is found between size effects, time relaxation and degenerate four wave mixi...

We study the flow map associated to the cubic Schrödinger equation in space dimension at least three. We consider initial data of arbitrary size in Hs, where 0 < s < sc, sc the critical index, and perturbations in Hσ , where σ < sc is independent of s. We show an instability mechanism in some Sobolev spaces of order smaller than s. The analysis relies on two features of super-critical geometric...

A method is proposed for finding exact solutions of the nonlinear Schr~dinger equation. It uses an ansatz in which the real and imaginary parts of the unknown function are connected by a linear relation with coefficients that depend only on the time. The method consists of constructing a system of ordinary differential equations whose solutions determine solutions of the nonlinear Schr~dinger e...

In this paper we give some ideas that can be useful to solve Schrodinger equations in the case when the Hamiltonian contains a large term. We obtain an expansion of the solution in reciprocal powers of the large coupling constant. The procedure followed consists in considering that the small part of the Hamiltonian engenders a motion adiabatic to the motion generated by the large part of the same.

A numerical behavior of a KdV combined mKdV equation is obtained using the Melnikov method. Melnikov method is proved to be elegant, and successful alternative to characterizing the complex dynamics of multi-stable oscillators. Based on the Melnikov theory we present the homoclinic and heteroclinic orbits in the unperturbed system. It is show us whether the system is chaotic or not. In this wor...

The inverse scattering transform for an integrable discretization of the defocusing nonlinear Schrodinger equation with nonvanishing boundary values at infinity is constructed. This problem had been previously studied, and many key results had been established. Here, a suitable transformation of the scattering problem is introduced in order to address the open issue of analyticity of eigenfunct...