Some properties of the fractional Schrödinger equation are studied. We prove the Hermiticity of the fractional Hamilton operator and establish the parity conservation law for fractional quantum mechanics. As physical applications of the fractional Schrödinger equation we find the energy spectra of a hydrogenlike atom (fractional "Bohr atom") and of a fractional oscillator in the semiclassical a...

In this work, we explore a generalization of the Dirac and Klein–Gordon (KG) oscillators, provided with deformed linear momentum inspired in nonextensive statistics, that gives place to Morse potential relativistic contexts by first principles. (1 + 1)-dimensional case, oscillators are mapped into quantum potential. Using Pekeris approximation, (3 study thermodynamics S-waves states (l = 0) H 2...

We review the recent glueball mass calculations using an efficient method for solving the Schrödinger equation order by order with a scheme preserving the continuum limit. The reliability of the method is further supported by new accurate results for (1+1)-dimensional σ models and (2+1)-dimensional non-abelian models. We present first and encouraging data for the glueball masses in 3+1 dimensio...

(Abstract) The ordinary Schrödinger equation with minimal coupling for a nonrelativistic electron interacting with a single-mode photon field is not satisfied by the nonrelativistic limit of the exact solutions to the corresponding Dirac equation. A Schrödinger-like equation valid for arbitrary photon intensity is derived from the Dirac equation without the weak-field assumption. The ”eigenvalu...

The canonical quantum theory of a free field using arbitrary foliations of a flat twodimensional spacetime is investigated. It is shown that dynamical evolution along arbitrary spacelike foliations is unitarily implemented on the same Fock space as that associated with inertial foliations. It follows that the Schrödinger picture exists for arbitrary foliations as a unitary image of the Heisenbe...

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...

The orbit of a classical particle in a central field, due to the angular momentum conservation, must lie in a plane perpendicular to the angular momentum. However, the orbit is, in general, not closed. In classical mechanics there is a famous Bertrand’s theorem [1,2], which says that the only central forces that result in closed orbits for all bound particles are the inverse square law and Hook...

Abstract In this paper, we investigate the effects of quantum confinement at the Si–SiO2 interface on the properties of MOSFETs with a channel length of 50 nm. To this end, we have developed a three-dimensional Poisson–Schrödinger solver, based on an approximation which allows us to decouple the Schrödinger equation into an equation in the direction perpendicular to the channel and an equation ...

We consider a controlled Schrödinger equation with a dipolar and a polarizability term, used when the dipolar approximation is not valid. The control is the amplitude of the external electric field, it acts non linearly on the state. We extend in this infinite dimensional framework previous techniques used by Coron, Grigoriu, Lefter and Turinici for stabilization in finite dimension. We conside...

The numerical approximation of the solution of the time-dependent Schrödinger equation arising in ultrafast laser dynamics is discussed. The linear electronic Schrödinger equation is reduced to a computationally tractable, lower dimensional system of nonlinear partial differential equations by the multi-configuration timedependent Hartree-Fock method (MCTDHF). This method uses an ansatz for the...