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A class of periodic solutions of the nonlinear Schrodinger equation with non- Hermitian potentials are considered. The system may be implemented in planar nonlinear optical waveguides carrying an appropriate distribution of local gain and…
Bound states of the power-law and logarithmic potentials are calculated using a generalized pseudospectral method. The solution of the single-particle Schr\"odinger equation in a nonuniform and optimal spatial discretization offers accurate…
We consider systems of weakly coupled Schr\"odinger equations with nonconstant potentials and we investigate the existence of nontrivial nonnegative solutions which concentrate around local minima of the potentials. We obtain sufficient and…
We focus on a recently developed generalized pseudospectral method for accurate, efficient treatment of certain central potentials of interest in various branches in quantum mechanics, usually having singularity. Essentially this allows…
A modified perturbation theory in the strength of the nonlinear term is used to solve the Nonlinear Schroedinger Equation with a random potential. It is demonstrated that in some cases it is more efficient than other methods. Moreover we…
An upgraded concept of solvability of Schr\"{o}dinger-type equations is proposed. In a broader methodical context of non-perturbative quantum theory the innovation involves potentials which are piece-wise analytic yielding differential…
This paper aims to investigate the pseudo-modes of the one-dimensional Schr\"odinger operator with complex potentials, focusing on the behavior of the resolvent norm along specific curves in the complex plane and assessing the stability of…
The asymptotic iteration method is used to find exact and approximate solutions of Schroedinger's equation for a number of one-dimensional trigonometric potentials (sine-squared, double-cosine, tangent-squared, and complex cotangent).…
Schr\"odinger equation for two center Coulomb plus harmonic oscillator potential is solved by the method of ethalon equation at large intercenter separations. Asymptotical expansions for energy term and wave function are obtained in the…
For the first time, the general nonlinear Schr\"odinger equation is investigated, in which the chromatic dispersion and potential are specified by two arbitrary functions. The equation in question is a natural generalization of a wide class…
Li\'enard-type nonlinear one-dimensional oscillator is quantized using van Roos symmetric ordering recipe for the kinetic-like part of the new derived Hamiltonian. The corresponding Schr\"odinger equation is exactly solved in momuntum space…
An approach based on splitting the reaction potential into a finite range part and a long range tail part to describe few-body scattering in the case of a Coulombic interaction is proposed. The solution to the Schr\"odinger equation for the…
We use special quadrature formulas for singular and hypersingular integral to numerically solve the Schr\"{o}dinger equation in momentum space with the linear confinement potential, Coulomb and Cornell potentials. It is shown that the…
We consider nonlinear Schrodinger equations with either local or nonlocal nonlinearities. In addition, we include periodic potentials as used, for example, in matter wave experiments in optical lattices. By considering the corresponding…
We develop a modified semi-classical approach to the approximate solution of Schrodinger's equation for certain nonlinear quantum oscillations problems. At lowest order, the Hamilton-Jacobi equation of the conventional semi-classical…
We analyze the calculation of bound states for a nonrelativistic spin-half neutral particle under the influence of a Coulomb-like potential induced by Lorentz symmetry breaking effects. We show that the truncation condition proposed by the…
We introduce new coherent states and use them to prove semi-classical estimates for Schr\"odinger operators with regular potentials. This can be further applied to the Thomas-Fermi potential yielding a new proof of the Scott correction for…
The celebrated Kronig-Penney model traditionally has been formulated with square well potentials representing atomic centres. Here, we use a slightly more realistic potential, the truncated harmonic oscillator, in lieu of square well…
We present a method for treatment of three charged particles. The proposed method has universal character and is applicable both for bound and continuum states. A finite rank approximation is used for Coulomb potential in three-body system…
We use the "tridiagonal representation approach" to solve the time-independent Schr\"odinger equation for the bound states of generalized versions of the trigonometric and hyperbolic P\"oschl-Teller potentials. These new solvable potentials…