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We propose a new variational approach to finding multiple critical points for strongly indefinite problems without assuming the weak upper semicontinuity on the variational functionals. By this approach, we obtain the existence of…

Functional Analysis · Mathematics 2024-04-04 Long-Jiang Gu , Huan-Song Zhou

In this study, we present analytical solutions of the Schr\"odinger equation with the Multiparameter potential containing the different types of physical potential via the asymptotic iteration method (AIM) by applying a Pekeris-type…

Quantum Physics · Physics 2017-02-02 Ahmet Taş , Ali Havare

The spectrum of r-1 and r-2 type potentials of diatomic molecules in radial Schrodinger equation are calculated by using the formalism of asymptotic iteration method. The alternative method is used to solve eigenvalues and eigenfunctions of…

Mathematical Physics · Physics 2016-11-26 Ozgur Oztemel , Eser Olgar

A new solvable hyperbolic single wave potential is found by expanding the regular solution of the 1D Schr\"odinger equation in terms of square integrable basis. The main characteristic of the basis is in supporting an infinite tridiagonal…

Mathematical Physics · Physics 2015-05-18 H. Bahlouli , A. D. Alhaidari

In this paper, we investigate the revivals of the one-dimensional periodic Schr\"odinger equation with a piecewise $C^2$ potential function. As has been observed through numerical simulations of the equation with various initial data and…

Analysis of PDEs · Mathematics 2025-04-23 Dinh-Quan Tran , Peter J. Olver

In this paper, we investigate the Schr\"odinger equation for a class of spherically symmetric potentials in a simple and unified manner using the Lie algebraic approach within the framework of quasi-exact solvability. We illustrate that all…

Quantum Physics · Physics 2016-07-18 Hossein Panahi , Marzieh Baradaran

In this paper, we determine the spectral instability of periodic odd waves for the defocusing fractional cubic nonlinear Schr\"odinger equation. Our approach is based on periodic perturbations that have the same period as the standing wave…

Analysis of PDEs · Mathematics 2023-10-13 Handan Borluk , Gulcin M. Muslu , Fábio Natali

The radial Schrodinger equation for a spherically symmetric potential can be regarded as a one dimensional classical harmonic oscillator with a time-dependent spring constant. For solving classical dynamics problems, symplectic integrators…

Computational Physics · Physics 2009-11-11 Siu A. Chin , Petr Anisimov

We consider travelling periodical and quasiperiodical waves in single mode fibres, with weak birefringence and under the action of cross-phase modulation. The problem is reduced to the ``1:2:1" integrable case of the two-particle quartic…

High Energy Physics - Theory · Physics 2019-08-15 P L Christiansen , J C Eilbeck , V Z Enolskii , N A Kostov

The polynomial solution of the Schrodinger equation for the Pseudoharmonic potential is found for any arbitrary angular momentum $l$. The exact bound-state energy eigenvalues and the corresponding eigen functions are analytically…

Quantum Physics · Physics 2007-05-23 Sameer M. Ikhdair , Ramazan Sever

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…

Quantum Physics · Physics 2015-06-16 Amlan K. Roy

We apply the asymptotic iteration method (AIM) to obtain the solutions of Schrodinger equation in the presence of Poschl-Teller (PT) potential. We also obtain the solutions of Dirac equation for the same potential under the condition of…

Quantum Physics · Physics 2015-06-16 Sameer M. Ikhdair , Babatunde J. Falaye

We study the spherical quantum pseudodots in the Schrodinger equation using the pseudo-harmonic plus harmonic oscillator potentials considering the effect of the external electric and magnetic fields. The finite energy levels and the wave…

Quantum Physics · Physics 2019-04-15 Mahdi Eshghi , Sameer M. Ikhdair

By using quasi--derivatives we develop a Fourier method for studying the spectral gaps of one dimensional Schr\"odinger operators with periodic singular potentials $v.$ Our results reveal a close relationship between smoothness of…

Spectral Theory · Mathematics 2009-03-31 Plamen Djakov , Boris Mityagin

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…

Exactly Solvable and Integrable Systems · Physics 2024-12-03 Andrei D. Polyanin , Nikolay A. Kudryashov

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…

Mesoscale and Nanoscale Physics · Physics 2013-08-30 Yevgeny Krivolapov , Shmuel Fishman , Avy Soffer

We present a new numerical method for accurate computations of solutions to (linear) one dimensional Schr\"odinger equations with periodic potentials. This is a prominent model in solid state physics where we also allow for perturbations by…

Numerical Analysis · Mathematics 2012-05-03 Zhongyi Huang , Shi Jin , Peter Markowich , Christof Sparber

A new pseudoperturbative (artificial in nature) methodical proposal [15] is used to solve for Schrodinger equation with a class of phenomenologically useful and methodically challenging anharmonice oscillator potentials V(q)=\alpha_o q^2 +…

Quantum Physics · Physics 2009-11-06 Omar Mustafa , Maen Odeh

A new approximation scheme to the centrifugal term is proposed to obtain the $l\neq 0$ bound-state solutions of the Schr\"{o}dinger equation for an exponential-type potential in the framework of the hypergeometric method. The corresponding…

Quantum Physics · Physics 2015-05-13 Sameer M. Ikhdair , Ramazan Sever

We discuss a new approach to solve the low lying states of the Schroedinger equation. For a fairly large class of problems, this new approach leads to convergent iterative solutions, in contrast to perturbative series expansions. These…

Quantum Physics · Physics 2009-11-10 R. Friedberg , T. D. Lee