In this study, we will construct numerical techniques for tackling the logarithmic Schrödinger’s nonlinear equation utilizing explicit scheme and Crank-Nicolson of finite difference method. These schemes be subjected to accuracy stability tests before being used. Efficacy robustness under consideration demonstrated using an exact solution, one-Gausson, as well conserved quantities. Interaction ...

The celebrated Black-Scholes di.erential equation provides for the price of a 0nancial derivative. The uncertainty environment of such option price can be described by the classical ‘bit’: a system with two possible states. This paper argues for the introduction of a di.erent uncertainty environment characterized by the so called ‘qubit’. We obtain an information-based option price and discuss ...

We prove a criterion for absence of eigenvalues for one-dimensional Schrr odinger operators. This criterion can be regarded as an L 1-version of Gor-don's theorem and it has a broader range of application. Absence of eigenvalues is then established for quasiperiodic potentials generated by Liouville frequencies and various types of functions such as step functions, HH older continuous functions...

We obtain necessary and sufficient conditions for emerging of small eigen-value for Schrödinger operator on plane under local operator perturbations. In the case the eigenvalue emerges we construct its asymptotics. The examples are given.

Two recent investigations are reviewed: quantum effects for DNA aggregates and scars formation on virus capsids. The possibility that scars could explain certain data recently obtained by Sundquist’s group in electron cryotomography of immature HIV-1 virions is also briefly addressed. Furthermore, a bottom-up reflection is presented on the need to invent new physics to pave the way to a rigorou...

We regard the Schrr odinger{Poisson system arising from the modelling of an electron gas with reduced dimension in a bounded up to three{ dimensional domain and establish the method of steepest descent. The electro-static potentials of the iteration scheme will converge uniformly on the spatial domain. To get this result we investigate the Schrr odinger operator, the Fermi level and the quantum...

We consider the periodic Schrr odinger operator ?+V (x) in R d , d 3 with potential V in the C. Feeerman-Phong class. Let be a periodic cell for V. We show that, for p 2 ((d ? 1)=2; d=2], there exists a positive constant " depending only on the shape of , p and d such that, if lim sup r!0 sup x2 r 2