In this paper, we study the existence of infinitely many weak solutions to a fractional Kirchhoff-Schr\"{o}dinger-Poisson system involving singularity, i.e. when $0<\gamma<1$. Further, obtain solution with strong $\gamma>1$. We employ variational techniques prove and multiplicity results. Moreover, $L^{\infty}$ estimate is obtained by using Moser iteration method.

Interaction and correlation effects in quantum dots play a fundamental role in defining both their equilibrium and transport properties. Numerical methods are commonly employed to study such systems. In this paper we investigate the numerical calculation of quantum transport of electrons in spherical centered defect InGaAs/AlGaAs quantum dot (SCDQD). The simulation is based on the imaginary time...

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...